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Module PMR109


                           CHAPTER 8 :STATISTICS


1.1 Data – a collection of information or facts.
    Data can be collected by – Counting, Measuring, Observation, Interview or
    Questionnaires. The data collected should be recorded in Frequency Table
    by using a tally chart. A tally chart shown below :

     eg 1 : Tally Chart

                    Mark                Tally Marks
                     48
                     53
                     60
                     65
                     72

1.2 Frequency – the number of times a certain number, measurement, score
   or item occurs. Frequency can be easily obtained by using a tally chart
   shown by eg 1 and a frequency table is used to organize a set of data.
   The frequency table can be constructed either vertically or horizontally that
    shown below.

     eg 2 : Frequency Table

             Mark    Frequency
              48         5
              53         7              Mark          48   53   60    65   72
              60         4              Frequency     5    7    4      5    3
              65         5
              72         3


1.3 The ways to represent and interpret data :

A. Pictograms
   - represents data in the form of a picture diagram, use a picture or a
     symbol that is easily understood.

       eg 3 :
                       Group A
                       Group B
                       Group C
                                 represents 10 students




Statistics                              109
Module PMR110


B.     Bar Charts
       - represents data using vertical or horizontal bars. It is a frequency
         diagram using rectangles of equal width.
           eg 4 :

 School                                                                                     School



 160                                                                                        T


140
                                                                                            S
120


100                                                                                         R

 80

                                                                                            Q
 60


 40
                                                                                            P

 20

                                                                                                0        40   60   80   100   120    140   160    Number of
                                                                                                    20
  0                                                                        Number of                                                              Classrooms
           P        Q       R                             S       T        Classrooms




          - A dual bar chart can be constructed to represent two sets of data in the
            same chart by using separate bars or single bar.
           eg 5 :
                                                                                   School

 School
                                                                                  140


                                                                                  120
100
                                                                                  100
 80
                                                                                   80
 60
                                                                                   60

 40
                                                                                   40

 20
                                                                                   20


  0                                                                                 0
            P           Q       R                             Numbe r of                        P        Q         R
                                                                                                                                    Number of
                                                              Classrooms                                                            Class rooms




C.     Line Graphs
       - used to represent changes in data over a period of time. The data is
         first represented by points. Then line segments are drawn to join the
         points.
         eg 6 :
                                Sale of chocolate cakes




                                                      100
                                                       80
                                                       60
                                                       40
                                                       20
                                                              0                                     Days
                                                                  M T W T F S S
Statistics                                                                       110
Module PMR111



D.    Pie chart
     - a circle, divided into sectors of various sizes, used for illustration and
       comparison of different categories of data.
       For a quantity P, the angle of the sector representing P is

                             Frequency of P
       Angle of sector =                     × 360°
                             Total frequency
                           = Frequency of P × 360°

       eg 7 : Type of Food Sold in A Day
                                    Fried Rice


                 Curry                              Noodle
                 Noodle            60o        o     Soup
                                         40

                                    140o



                                   Fried Noodle

1.4 Mode, Median and Mean.

A Mode – the value or item which occurs most frequently or highest
        frequency. The mode can determine from a given set of data, a
        frequency table, a pictogram, a bar chart, a line graph or pie chart.
              eg8 : 7, 4, 3, 4, 8, 7, 5, 4, 3
                    mode = 4 ( frequency=3 )

B Median – the middle value when all the data are arranged in an increasing or
           decreasing order. If the number of values is odd, then the median
           is the middle value. If the number of values is even, then the
           median is the mean of the two middle values.
       eg 9a : 10g, 12g, 18g, 10g, 16g                  eg 9b : 10, 12, 18, 10, 16,14
               ⇒ 10, 10, 12, 16, 18                              ⇒ 10, 10, 12, 14, 16, 18
       Median = 12g                                     Median = (12+14) ÷ 2 = 13

       eg 9c :
             Score            1               2          3         4         5
             Frequency        4               6          7         1         3
         Total frequency = 4+6+7+1+3 = 21
         Median       = Number of the 11th score
                      =3
         eg 9d :
             Score            1               2          3         4         5
             Frequency        4               6          7         0         3
Statistics                                        111
Module PMR112


         Total frequency         = 4+6+7+0+3 = 20
         Median                  = Number of the 10th and 11th score
                                   2+3     5
                                 =      =     = 2.5
                                     2     2

C Mean – is the arithmetic average of a set of data.

         Mean = sum of all the values of data
                  total number of data

         eg 10a : 5, 2, 6, 3, 4, 6, 5, 2, 3

                  5+ 2+6+3+ 4+6+5+ 2+3
         mean =
                            9
                  36
                =    =4
                   9
         eg 10b :
                    Price (RM)     15    20    25    30    35
                    Frequency       3     4     2     4    3

                  (15 × 3) + (20 × 4) + (25 × 2) + (30 × 4)) + (35 × 3)
         Mean =
                                    3+ 4+ 2+ 4+3
                  45 + 80 + 50 + 120 + 105
                =
                              16
                  400
                =      = RM25
                   16

Example 1:                                       Exercise 1:

Day               Mon Tue Wed Thu                Grade                A   B   C     D      E
Absentees          10  7  12  13                 Frequency            3   8   14    9      6

The frequency table shows the                    The table shows the distribution of
number of absentees on four                      grades obtained by 40 students in
particular school days. Based on the             the PMR.
information given, find                          a) How many students obtained
                                                    either grade A or grade B?
a) the day with the highest number
    of absentees.
Solution                                         b) If the grade E is the failing grade,
a) Thursday                                         find the number of students who
                                                    passed.
b) the day with the lowest number of
   absentees.

Solution                                         c) Which grade has the highest
b) Tuesday                                          frequency?

Statistics                                    112
Module PMR113


Example 2 :

      Number of Tourists to an Island Resort
        1999

          2000

          2001

          2002

          2003

          2004

                       Represents 2000 tourist

The pictogram above shows the number of tourist to an island resort from
1999 to 2004.

a) Which year had the highest number of tourist?
Solution :
a) Year 2004

b) Find the total number of tourist for the two years which had the same
   number of tourist.

Solution :
b) The two years were 2000 and 2002.
   Total number of tourists for 2000 and 2002
   = 2(10x2000)
   = 40 000

c) What was the total number of tourists for the six years?

Solution :
c) Total number of symbols
   = 8+10+9+10+4+14
   = 55
   Total number of tourists = 55 x 2000
                            = 110 000

d) If each tourist spent an average of RM600 during their stay, calculate the
   total amount of money spent by tourist on the island in 2001.

Solution :
d) Number of tourists in 2001 = 9 x 2000
                              = 18 000
     Amount spent = 18 000 x 600
                   = RM 10 800 000
Statistics                           113
Module PMR114


Exercise 2 :

Monday

Tuesday

Wednesday

Thursday

Friday

           Represents 60 bowls
The pictogram shows the number of the bowls of noodles sold in a school
canteen from Monday to Friday.
a) Which day has the highest sales?



b) If the profit from each bowl of noodles sold is RM0.20, find the total profit
   for the five days.




c) Find the difference in the profits obtained from the sales on Monday and
   Friday.




Example 3 :                                                           Exercise 3:
Sales Figures of Watches for Five
Shops
                                                                                     Sales of Ice Cream for Six Days
                                                                              Day
                 Sale s Figur e s of Watche s for Fiv e Shops

                                                                        Sat
           450

           400
                                                                        Fri
           350

Numbe r    300
                                                                       Thurs
of         250
watche s
           200
                                                                        Wed
           150
           100
                                                                        Tue
           50

                                                                        Mon
                   A       B         C       D        E
                                                                               0    10   20   30   40   50   60   70   80   90   100   110   120 130 Value (RM)
                                  Shop




Statistics                                                      114
Module PMR115


The vertical bar chart given shows
the sales figures of watches for five         a) On which day did he sell the
shops in December.                               most ice cream?

a) What was the difference in
   number of watches sold between
   the shops with the highest and
   the lowest sales?

Solution :
a) Difference = 450 - 175                     b) How much more did he sell on
              = 275 watches                      Wednesday compare to
                                                 Monday?
b) If Shop E had an increase in
   sales of 20% the following month,
   while Shop A sold 30 fewer
   watches, what was the total sales
   for the two shops?

Solution :
b) Shop E :
   120% of 400 = 480 watches                  c) Calculate his total sales for six
                                                 days.
    Shop A :
    250 – 30 = 220 watches

    Total sales for the two shops
    = 480 + 220
    = 700 watches
                                              d) If his total profit from his ice
                                                 cream sales was 15%, calculate
c) If the average value of a watch               the vendor’s profit on Thursday.
   was RM150, calculate the total
   value of the watches sold by all
   five shops in December.

Solution :
c) Total number of watches
   = 250+ 175+ 450+ 325+ 400
   = 1600 watches

    Total value = 1600 x 150
                = RM240 000



The horizontal bar chart above
shows the sales of an ice cream
vendor for six days.

Statistics                              115
Module PMR116



Example 4 :                                                        Exercise 4 :
                            M age sh's Best 400 m Time s
                                                                                            Numbe r of Employe e s in Ne wTe ch
         59                                                                                 Company from 1999 to 2004
         58

         57
                                                                              400
         56

         55                                                                   350
         54
                                                                              300
         53
 Time
 (sec)   52                                                                    250
                                                                   Numbe r of
         51                                                        employe e s 200
         50
                                                                              150
         49

         48                                                                   100
         47
                                                                               50
         46
         45                                                                    0
              1999   2000     2001      2002   2003   2004                           1999      2000     2001     2002    2003     2004
                                Ye ar
                                                                                                         Ye ar

The line graph given shows
Magesh’s best times for the 400m                                   The line graph above shows the
track event over a period of 6 years.                              number of employees in NewTech
                                                                   Company from 1999 to 2004.
a) From which year onwards did he
   run below 55 seconds?                                           a) How many employees were there
Solution :                                                            in 1999?
a) From 2001 onwards.

b) What was his improvement in
   time after 6 years of training?
                                                                   b) When was there the greatest
Solution :                                                            increase in the number of
b) Improvement                                                        employees ?
   = Slowest time – Fastest time
   = 57.5 – 49

c) What was his percentage
   improvement in time from 2002 to                                c) How many more employees were
   2004?                                                              there in 2004 compared to 2001?

Solution :
Difference in time
    = 52 - 49
    = 3 seconds

     Percentage improvement in time
        3
     =    × 100 %
       52

     = 5.77%


Statistics                                                   116
Module PMR117


Example 5 :                                    Exercise 5 :
                                                Total Car Sales in Malaysia in 2003


                                                              Others
             tea                                              56.3°
                         milk                                               Proton
                                                                            166.7°
                                                       Perodua



       cof f ee    chocolate




                                                                 Hy undai

All the Form 3 students took part in a
                                                                                 1
survey on their favourite hot drinks.          Given that Perodua cars took up
The results were shown in the pie                                                3
chart above.                                   of the nation’s total car sales and
                                               Hyundai’s sales was RM21.5 billion.
a) Which drink was least preferred
   by the Form 3 students?                     a) Find the angle of the sector for
                                                  i)     Perodua cars.
Solutions :                                       ii)    Hyundai cars.
a) Milk was least preferred by Form
   3 students.

b) Which was the most popular
   drink among the Form 3                      b) How much was the total car sales
   students?                                      in 2003?

Solutions :
Tea was the most popular drink
among the students.

c) How many percent of            the          c) How much was the sales of
   students like hot chocolate?                   Proton cars in 2003?


Solutions :
b) Percentage of students who like
   hot chocolate
   = 90o
     360o      X 100%

    = 25%




Statistics                               117
Module PMR118


Example 6:                                       used for represent the price of
Mr Song bought a basket of                       the watermelon.
watermelons with RM150. He sold
them according to their quantities as         d) Find the mean price of the
shown in the table below.                        remaining watermelons, if Mr
 Price       1.50 2.00 2.50 3.00                 Song had only sold 70 fruits with
 (RM)                                            a collection of RM141.
 Number       42     12     x     10
 of fruits                                    Solution :
The total sales for all the                   d) Number of fruit remaining
watermelons was RM207.                           = 100 -70
                                                 = 30
a) Find the value of x.
Solution :                                       Mean price of the remaining
a) Total sales = 42 x 1.50 + 12 x                watermelon :
   2.00 + x x 2.50 + 10 x 3.00                     207 − 141
   207 = 117 +2.5x                               =
                                                      30
   2.5 x = 207 – 117                             = RM 2.20
      x = 90/2.5
          = 36
                                              Exercise 6 :
b) Find the mean, mode and
   median of the price of the                 The table below shows the
   watermelons.                               performance of a group of students
Solution :                                    in a test.
b) Total number of fruits
   = 42+12+36+10                               Scores        6    7     8    9     10
   = 100                                       Frequency     2    4     x    5     2
                Total collection
   Mean =
            Total number of fruits
           RM 207                             a) Given that the modal score is 8
         =                                       and the mean score is greater
             100
         = RM 2.07                               than the mode, find the least
   Mode = RM1.50                                 possible value for x. Hence, find
                                                 its mean.
              2.00 + 2.00 
   Median =                                 .
                   2      
           = RM2.00

c) Among the mean, mode and
   median, which is suitable to be            b) If another 6 students joined the
   used for representing the price of            group and the scores obtained
   the watermelons?                              are
Solution :                                           9, 10, 9, 10, 9, 10
c) Mode is not suitable as there are             Find the mode, median and
   58 fruits costing more than                   mean of the score.
   RM1.50. Therefore, mean and
   median are both suitable to be

Common Errors
Statistics                              118
Module PMR119


1. Obtaining information from a pictogram.
                              Group A
                              Group B
                                        Represent 50 students
Errors                                                    Correct Steps
Total numbers of students                                 Total numbers of students
= 4+6                                                     = ( 4+6) x 50
= 10                                                      = 10 x 50 = 500

2. Error in determining the mode in a frequency table.
 Marks                   0            1              2                     3               4
 Frequency               3            4              3                     1               5
Errors                                                    Correct Steps
The mode is 3.                                            The mode is 4.
The mode is 5.

3. Error in determining the median of a set data.
Errors                                    Correct Steps
5, 2, 4, 8, 2, 3, 1 (data not rearrange   1, 2, 2, 3, 4, 5, 8
in order)                                 Median = 3
Median = 8
4.
 Salary               Less than         RM1001 to          RM1501 to            RM2001 to          More than
                       RM1000            RM1500             RM2000               RM2500             RM2500
 Frequency                   14            118                  10                   5                4
The frequency table above shows the salaries of the staff in Super Home
Products Company. Find the number of staff whose salaries are less than
RM2000 per month.
Errors                                                    Correct Steps
Number of staff whose salaries are                        Number of staff whose salaries are
less than RM2000 per month                                less than RM2000 per month
= 14 + 118                                                = 14 + 118 +10
= 132                                                     = 142
5. The combined bar chart shows the sales figures for HIQ Bookstore from
   January to April. Find the total number of non-fiction books sold.
                 Sales Figures from January to Apri l for HI Q bookstore
         Month


      Apr.




      Mar.




      Feb.




       Jan




             0      20        40      60       80         100        120       140
                                                                               Number of
                                                                               books



Errors
Statistics                                          119
Module PMR121


Total number of non-fiction books             Total number of non-fiction books
sold                                          sold
= 100 + 130 + 100 + 110                       = 60 + 80 + 70 + 90
= 440                                         = 300
Correct Steps

5. The table shows the distribution of the scores obtained in tossing a dice 30
   times. Find the mean score of each toss.

                  Score            1    2         3     4         5   6
                  Frequency        5    4         6     8         3   4

Errors                                        Correct Steps
          1+ 2 + 3 + 4 + 5 + 6                Mean
Mean =
          5+ 4+ 6+8+3+ 4                        1(5) + 2(4) + 3(6) + 4(8) + 5(3) + 6(4)
                                              =
        = 0.7                                            5+ 4+6+8+3+ 4
                                              = 3.4

Extra Exercise

1 Mode :
a.   20 g, 50 g, 30 g, 70 g, 50 g,
     40 g, 30 g, 60 g, 50 g, 60 g,
     50 g, 60 g
         Mode = _____ g

b.       15 mm, 18 mm, 12 mm, 13 mm, 15mm,
         17 mm, 12 mm, 16mm, 15 mm, 13 mm,
         14 mm, 15 mm
         Mode = ______ mm

c.       4, 5, 6, 2, 1, 4, 6, 7, 5, 6
         Mode =

d.
             Number of matches played         1         2         3   4       5
                    Frequency
                                              1         4         3   2       3

         Mode = _______matches

e.
         Height ( cm )      120   121   122       123       124
             Frequency        2   9     7         3         4

         Mode =          cm

Statistics                              121
Module PMR121


f.
             Number Of goals        0       1      2       3       4
               Frequency            2       5      4       6       4

         Mode =         goals

2. Median
a.       4, 2, 5, 4, 7, 2, 1                      c. 2kg, 4kg, 1kg, 5kg, 4kg, 2kg
         Median =                                          Median =



b.       9, 2, 7, 1, 8, 9, 0                      d. 30m, 10m, 30m, 10m, 40m
         Median =                                          Median =

e.
        Number Of goals         0       1   2      3       4

        Frequency               1       5   4      4       3

         Total frequency = 1 + 5 + 4 + 4 + 3 =
         Median = Number of goals of the ___ th Frequency
                  =    goals

f.
              Grade                 A       B          C       D       E
         Numbers of students        6       12         9       8       11

         Total frequency = 6 + 12 + 9 + 8 + 11 =

         Median =


3. Mean ;
a.    21, 30, 25, 27, 31, 34                      b.       7 ,4 , 6 ,8 ,5 ,7 , 5

         Mean =                                            Mean =

c.
        Mass (g)           5    6       7   8
        Frequency          5    2       6   7
         Mean     =



Statistics                                  121
Module PMR122


4. The pictogram in Diagram below shows the number of durians sold by
   three fruits sellers. Calculate the total number of durians sold by three of
   them.

             Samad
             Chong
             Muthu
                                            represents 10 durians


5.
             Sale of chocolate cakes




                                   100
                                    80
                                    60
                                    40
                                    20
                                       0                         Days
                                           M T W T F S S
      The line graph shows the sale of chocolate cakes in a week. Find the
      difference between the highest sales and the lowest sales in the week.



6.
                                            70

                                            60
                                            50

                                            40
                                            30

                                            20
                                            10

                                            0                                        Day
                                                 M on   Tue s   We d    Thur   Fri

      The line graph shows the number of cars parked at Jeti Lumut over a
      period of five days. Each car is charged RM 8 per day. What is the total
      collection for the five days?


7             2 1 3 4 6 8 8 7 5 4
              5 4 3 1 2 1 1 4 2 4
      The data shows the scores obtained by 20 pupils in a game.

     a) By using the data given, complete the following table.
     Score          1      2      3    4      5      6      7                                8
     Frequency

     b) State the mode

Statistics                                                      122
Module PMR123


8. The mean of 5, y, 2y, 3y, 12,12, 15, 20 is 11. Find the value of y.


9. Calculate the difference between mean and median of the numbers
       5, 11, 20, 23, 15, 9, 3, 18.


10. Find the difference between mode and median of the numbers
       4, 3, 5, 9, 9, 9, 3, 7, 9.


11. Given that the mean of 3, 5, 10, 2, x, 15, y is 8, find the value of x+y.


12. The pie chart shows the number of coloured balls in a store.
                                        Green

                                    8
             Purple
                                                White
                      12
                                         6


                               10

                           Black
         Calculate the angle of the sector which represents black balls.


13. Diagram below is a line graph which shows the number of residents in a
      town from 1997 to 2004.




        a) During which year did the number of residents increase the most?


         b) How many residents were there in the town at the beginning of
            2001?

        c) Calculate the percentage increase of residents during the year 2002.


Statistics                                        123
Module PMR124


Questions based on PMR Format

1. The pictogram below shows the number of cars sold by Syarikat Maju
    Jaya from year 2004 to 2007.


              2004

              2005

              2006

              2007

                           Represents 50 cars.

    a) Number of cars sold in year 2006 = ______________



    b) If 200 cars were sold in year 2005, complete the pictogram above.




2. The frequency table below shows the marks obtained by 40 students from
    form 3 Budiman in the first round of a mathematics quiz.


              Score        1       2         3      4          5       6


             Number of     3       8         5      12         7       5
              students

    a) If students who get more than four marks will go on to the next round,
       how many students never made to the second round?




     b) Calculate the percentage of student that can go to the second round.




Statistics                             124
Module PMR125


3. The pie chart below shows the favourite colours chosen by a group of car
    owners.



                                                  Tomato Re d
                                                     12

                            Golde n Ye llow
                                24
                                                   Lime Gre e n
                                                        8

                                       Sky b lue
                                         16



     a) Find the angle of sector for cars with Golden Yellow colour.


     b) Calculate the percentage of cars with Tomato Red colour.



4. The bar chart below shows number of books read by form one, form two
    and form three students in SMK Sinar Mutiara for the past two months.
               Nu m b er
               of books
                                  Nilam 2008
                   35

                   30

                   25

                   20
                                                                      Sain s

                   15
                                                                      English
                   10

                   5


                        0
                            1           2               3

                                     For m


       a) Base on the bar chart above, complete the table below.

             Form                                 1               2            3
             Number of books

       b) Find the difference between Science and English books read by all
           students.




Statistics                                  125
Module PMR126


5. 21 , 13, 16, 19, 11, 16, 16

     Base on the data above, determine:
     a) the mode




    b) the median




6. The bar chart below shows the population of Kampung Selangkah,
    Kampung Temai, Kampung Dusun and Kampung Air.

             Number of resident


                 400




                 300




                 200                                              m ale

                                                                  fe m ale

                100




                  0

                        Kam pung Kam pung Kam pung Kam pu ng
                        Se langk ah Te m ai Du sun Air



      a) Find the total number of male in all the four Kampung.




       b) Find the percentage of female to the whole population?




Statistics                                   126
Module PMR127


7.

     Class                    Raden Mayang Bahagia                           Adil             Jujur     Iklas

     Collection(RM)
                                   200        300              50            250              100        310


       Based on the table above, complete the bar charts below.

                   (RM)                  CLASS FUND


             350

             300

             250

             200

             150

             100

             50

               0                                                                                    CLASS
                          Rad en    Mayan g    Bahagia       Adil        Jujur        Iklas




8.


      Number of points                        10     20             30           40           50       60
      Number of students                      5          4          7            5             6        3

      The frequency table above shows the marks obtained by a group of
       students in a marching competition.

      a) Find the number of students involved in the event.




      b) Find the mean point from the table.




Statistics                                           127
Module PMR128


9.


     2001

     2002

     2003

     2004

     2005


                 Represents 25 computers

     a) The pictograph above shows the sale of computers by Syarikat Indah
        Computer in five years . Complete the pictograph if the number of
         computers sold in year 2003 were 100 sets.




     b) Find the total number of computers sold in five years.




10.

        Number of books        1       2       3        4        5      6

      Number of students       2       5       8        3        6      7


     The frequency table above shows the number of books read by students in
     form 3 Bahagia of SMK Pekan under “ PROJEK NILAM”.

     a) Find the number of students involved in “PROJEK NILAM”.




     b) Determine the mode.




Statistics                             128
Module PMR129


11. The following data shows the marks obtained by pupils in a mathematic
      test:
                           23 27 26 27 22 22 22 23 26 25
                           24 23 27 27 26 23 22 22 25 25
                           22 27 26 26 26 25 24 24 23 22


              Marks        22       23           24    25         26        27

              Frequency

        a) Complete the frequency table above based on the data given


        b) Find the mode




12.
          21, 26, 29, 27, 21, 25, 25, 26, 29, 28, 30, 33, 23,29

      a) Find the mode



      b) Find the median




13. The table below shows the marks obtained in an English test.


              Marks         10        20          30        40         50


              Frequency     4         X           15        11          7


      a) Given that the number of frequency is 50, find the value of X




      b) Determine the mode.




Statistics                                 129
Module PMR130


14. The Pie chart below shows the subjects most liked by a group of 36
    students.




                          Science             Geography
                            120.0º            60.0°


                                                   History
                                     130.0°

                            Mathematics



     a) Find the number of students who like science .



     b) Find the percentage of pupils who like history.



15. The horizontal bar chart below shows the number of vehicles sold by three
    companies A, B and C.
                                       CAR         VAN



                C
         op y
        Cm a
          n




                B




                A



                    0       20                40             60        80
                                     No. of ve hicle s
                             Number of Vehicles

a). Calculate the number of vehicles sold by companies A and C.



b). Calculate the difference between the number of vans sold by companies
    B and C.



Statistics                              130
Module PMR131


16. Diagram below is a line graph which shows the number of residents in
    village X and village Y from 1998 to 2004.



                                                                Y

                                                                 X




         a) In which year the difference in the number of residents between
             village X and village Y is 1 500?




         b) How many residents are there in village Y in the year 2002?




         c) Calculate the percentage increase in the number of residents in
            village X from 2000 to 2002.




Statistics                             131
Module PMR132


PMR past year questions

     2004

     1. The data in Diagram 5 shows marks obtained by 20 participants in a
        quiz.

               1       4      6    5      4       6       3       5      4     6
               2       1      2    4      6       1       2       4      2     3

         a) Using the data, complete the frequency table in the answer space.
         b) State the mode.                                       [3 marks]

         Answer :
         a)
            Marks             1     2         3       4       5          6
            Frequency

         b)


     2. Table 1 shows the number of books in the reading corners of three
         classes.
                        Class                Number of Books
                        Aman                         75
                        Bestari                      60
                       Cerdas                        90
                                             Table 1
        The information for Bestari class is shown fully in the pictograph in the
        answer space. Complete the pictograph to represent all the information
        in Table 1.                                                      [3
        marks]

         Answer :


                     Number of books in the reading corners

                    Aman

                    Bestari

                    Cerdas


                              Represents _______ books



Statistics                              132
Module PMR133



     2005

     3. Table 1 shows the number of students who play four types of games.

                 Types of games         Number of students
                 Ping-pong                      8
                 Badminton                      15
                 Hockey                         25
                 Handball                       12
                              Table 1

         The information for badminton is shown fully in the pie chart in the
         answer space.
         Complete the pie chart to represent all the information in Table 1.
                                                                  [5 marks]


         Answer :




                                               Badminton

                                                   90 °




Statistics                               133
Module PMR134



     2006

     4. Table 1 shows the profit made from the sales of nasi lemak at a stall
        over 5 days.

                Day        Monday   Tuesday    Wednesday   Thursday      Friday
             Profit (RM)     32      40           24           28            28
                                     Table 1

         On Diagram 4 in the answer space, draw a line graph to represent all
         the information in Table 1. Use the scale 2 cm to RM8 on the vertical
         axis.
                                                                  [5 marks]

         Answer :




              Profit (RM )




               40



               32




               24



               16



                8



                                                                                  Day
                             Mon     Tu e       We d       Th ur      Fr i

                                    Diagram 4



Statistics                             134
Module PMR135


     5. Diagram 5 is a pie chart which shows the number of pupils in five
        group who complete an assignment during a motivational camp.


                                             Tuah
                                              10
                                                       Jebat
                                                        x
                                   Lekiu                       Diagram 5
                                    12
                                                     Kasturi
                                             Lekir    2x
                                              8




         It is given that the total number of pupils who complete the assignment
         is 36.
         a) Find the value of x.
         b) Calculate the angle of the sector representing the Tuah group.
             Show your working.
         c) State the mode of your data.
                                                                        [5 marks]
         Answer :
         a)

         b)

         c)

     2007

     6. Table 1 shows three activities participated by a group of 50 students.

                     Activities             Number of
                                             students
                       Chess                    24
                      Hockey                    M
                       Choir                   18
                                  Table 1

             a) Find the value of M
             b) Hence , represent all the data by drawing a bar chart in the answer
                space.                                                     [4
                marks]

         Answer :
         a)


Statistics                                   135
Module PMR136


        b)


                Numbe r of stude nts

                 28



                 24



                 20



                 16



                 12



                  8



                  4



                  0                                                 Activ itie s
                              Cheess        Hockey         Choir




     7. Diagram 3 shows the scores obtained by 15 Police Cadets in a
        shooting competition.


                      1, 2, 4, 3, 1, 2, 4, 1, 3, 2, 1, 3, 1, 1, 3

                                     Diagram 3

             a) Using the data, complete the frequency table in the answer space.

             b) State the median.                                                  [ 3 marks]




Statistics                                       136
Module PMR137


         Answer :

         a)
                               Score                Frequency
                                 1
                                 2
                                 3
                                 4

         b) Median =

     2008
     8. Table 15 in the answer space shows the number of gold medals
        obtained by four schools in a sports competition. The information for
        school L is shown fully in the pie chart in Diagram 15.

             Complete
             a) the angles of the sectors for school M and school N in Table 15.
             b) the pie chart in Diagram 15 to represent all the information in Table
                15.                                                        [5 marks]

         Answer:
         a)
             School              Number of gold             Angle of sector
                                    medals
                   K                 10                           300

                   L                     60                      180o
                   M                     20

                   N                     30


         b)




                                   L

                                    180o




                                       Diagram 15


Statistics                                    137
Module PMR138


                      CHAPTER 8 : STATISTICS
                           ANSWERS

Exercise 1                           1f. 3
a. 11
b. 34                                2a.   4
c. Grade C                           2b.   7
                                     2c.   3
Exercise 2                           2d.   30m
a. Monday                            2e.   17, 9 , 2
b. RM288                             2f.   46, C
c. RM24
                                     3a. 28
Exercise 3                           3b. 6
a. Saturday                          3c. 6.75
b. RM 45
c. RM 530                            4. 120
d. RM11.25
                                     5. 80
Exercise 4
a. 25                                6. RM2000
b. between 2003 and 2004
c. 275                               7a.

Exercise 5                            Score            1   2   3     4   5   6     7   8
ai. 120o                              Frequency        4   3   2     5   2   1     1   2
aii. 17o                             7b. 4
b. RM 455.30
c. RM 210.80                         8.    4

Exercise 6.                          9.    0
a. x= 6
   mean= 8.05                        10. 2
b. mode = 9
   median = 9                        11. 21
   mean = 8.4
                                     12. 100o
Extra Exercise
1a. 50                               13a. 1997 and 2000
1b. 15                               13b. 28500
1c. 6                                        1
1d. 2                                13c. 9
                                            11
1e. 121




Statistics                     138
Module PMR139


Questions based on PMR Format

1. a) 250                                   9. a)       Draw 2 symbols correctly
   b) 4 symbols drawn                          b)       500 computers

2. a) 28 students                           10. a) 31
   b) 30%                                       b) 3

3. a)         144º                          11. a) 7, 5 ,3, 4, 6, 5
    b)        20%                               b) 22

4.   a) 45, 35, 45                          12. a) 29
     b) 15                                      b) 26.5

5.   a) 16                                  13. a)       13
     b) 16                                      b)       30

6.   a) 650                                 14. a) 12 students
     b) 43.48                                   b) 13.9%

7.   Draw the bars representing             15. a) 200
     Mayang, Adil and Jujur correctly           b) 10

8.   a) 30                                  16. a) year 2001
     b) 34                                     b) 4750
                                               c) 60%



PMR Past Year Questions
1. a)
    Marks        1           2          3           4         5       6
    Frequency    3           4          2           5         2       4
   b) 4

2. Number of books in the reading corners

             Aman

         Bestari

         Cerdas

                          Represents ___30____ books




Statistics                              139
Module PMR140


3.


                                        Ping
                                        Pong             Badminton
                                                                      c1
                                                48 °
                                                         90 °

                                              150°
                                                         72 °
                                   Hockey
                                                              Hand ball




4.

             Profit (RM )




             40



              32



             24



              16



               8



                                                                                    Day
                            Mo n       Tu e            We d        Th ur   Fr i

                                      Diagram 4


5. a) 2
   b) 100o
   c) Lekiu




Statistics                                       140
Module PMR141



6.        a) 8
6.        b)
                          Numbe r of stude nts

                          28



                          24



                          20



                          16



                           12



                           8



                           4



                           0                                                  Activ itie s
                                    Cheess        Hockey          Choir




7. a)
                                Score                             Frequency
                                  1                                   6
                                  2                                   3
                                  3                                   4
                                  4                                   2
      b)     2

8. a) a)
                                    Number of gold
                 School                                                         Angle of sector
                                       medals
                   K                             10                                           300

                   L                             60                                          180o

                   M                             20                                          600

                   N                             30                                          900
     b)

                                                            K
                                                           30 °
                                                                          M
                                                                °
                                                              60°
                                          L         °
                                                 180°
                                                             °
                                                           90°

                                                                  N




Statistics                                            141

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Chapter 8 statistics

  • 1. Module PMR109 CHAPTER 8 :STATISTICS 1.1 Data – a collection of information or facts. Data can be collected by – Counting, Measuring, Observation, Interview or Questionnaires. The data collected should be recorded in Frequency Table by using a tally chart. A tally chart shown below : eg 1 : Tally Chart Mark Tally Marks 48 53 60 65 72 1.2 Frequency – the number of times a certain number, measurement, score or item occurs. Frequency can be easily obtained by using a tally chart shown by eg 1 and a frequency table is used to organize a set of data. The frequency table can be constructed either vertically or horizontally that shown below. eg 2 : Frequency Table Mark Frequency 48 5 53 7 Mark 48 53 60 65 72 60 4 Frequency 5 7 4 5 3 65 5 72 3 1.3 The ways to represent and interpret data : A. Pictograms - represents data in the form of a picture diagram, use a picture or a symbol that is easily understood. eg 3 : Group A Group B Group C represents 10 students Statistics 109
  • 2. Module PMR110 B. Bar Charts - represents data using vertical or horizontal bars. It is a frequency diagram using rectangles of equal width. eg 4 : School School 160 T 140 S 120 100 R 80 Q 60 40 P 20 0 40 60 80 100 120 140 160 Number of 20 0 Number of Classrooms P Q R S T Classrooms - A dual bar chart can be constructed to represent two sets of data in the same chart by using separate bars or single bar. eg 5 : School School 140 120 100 100 80 80 60 60 40 40 20 20 0 0 P Q R Numbe r of P Q R Number of Classrooms Class rooms C. Line Graphs - used to represent changes in data over a period of time. The data is first represented by points. Then line segments are drawn to join the points. eg 6 : Sale of chocolate cakes 100 80 60 40 20 0 Days M T W T F S S Statistics 110
  • 3. Module PMR111 D. Pie chart - a circle, divided into sectors of various sizes, used for illustration and comparison of different categories of data. For a quantity P, the angle of the sector representing P is Frequency of P Angle of sector = × 360° Total frequency = Frequency of P × 360° eg 7 : Type of Food Sold in A Day Fried Rice Curry Noodle Noodle 60o o Soup 40 140o Fried Noodle 1.4 Mode, Median and Mean. A Mode – the value or item which occurs most frequently or highest frequency. The mode can determine from a given set of data, a frequency table, a pictogram, a bar chart, a line graph or pie chart. eg8 : 7, 4, 3, 4, 8, 7, 5, 4, 3 mode = 4 ( frequency=3 ) B Median – the middle value when all the data are arranged in an increasing or decreasing order. If the number of values is odd, then the median is the middle value. If the number of values is even, then the median is the mean of the two middle values. eg 9a : 10g, 12g, 18g, 10g, 16g eg 9b : 10, 12, 18, 10, 16,14 ⇒ 10, 10, 12, 16, 18 ⇒ 10, 10, 12, 14, 16, 18 Median = 12g Median = (12+14) ÷ 2 = 13 eg 9c : Score 1 2 3 4 5 Frequency 4 6 7 1 3 Total frequency = 4+6+7+1+3 = 21 Median = Number of the 11th score =3 eg 9d : Score 1 2 3 4 5 Frequency 4 6 7 0 3 Statistics 111
  • 4. Module PMR112 Total frequency = 4+6+7+0+3 = 20 Median = Number of the 10th and 11th score 2+3 5 = = = 2.5 2 2 C Mean – is the arithmetic average of a set of data. Mean = sum of all the values of data total number of data eg 10a : 5, 2, 6, 3, 4, 6, 5, 2, 3 5+ 2+6+3+ 4+6+5+ 2+3 mean = 9 36 = =4 9 eg 10b : Price (RM) 15 20 25 30 35 Frequency 3 4 2 4 3 (15 × 3) + (20 × 4) + (25 × 2) + (30 × 4)) + (35 × 3) Mean = 3+ 4+ 2+ 4+3 45 + 80 + 50 + 120 + 105 = 16 400 = = RM25 16 Example 1: Exercise 1: Day Mon Tue Wed Thu Grade A B C D E Absentees 10 7 12 13 Frequency 3 8 14 9 6 The frequency table shows the The table shows the distribution of number of absentees on four grades obtained by 40 students in particular school days. Based on the the PMR. information given, find a) How many students obtained either grade A or grade B? a) the day with the highest number of absentees. Solution b) If the grade E is the failing grade, a) Thursday find the number of students who passed. b) the day with the lowest number of absentees. Solution c) Which grade has the highest b) Tuesday frequency? Statistics 112
  • 5. Module PMR113 Example 2 : Number of Tourists to an Island Resort 1999 2000 2001 2002 2003 2004 Represents 2000 tourist The pictogram above shows the number of tourist to an island resort from 1999 to 2004. a) Which year had the highest number of tourist? Solution : a) Year 2004 b) Find the total number of tourist for the two years which had the same number of tourist. Solution : b) The two years were 2000 and 2002. Total number of tourists for 2000 and 2002 = 2(10x2000) = 40 000 c) What was the total number of tourists for the six years? Solution : c) Total number of symbols = 8+10+9+10+4+14 = 55 Total number of tourists = 55 x 2000 = 110 000 d) If each tourist spent an average of RM600 during their stay, calculate the total amount of money spent by tourist on the island in 2001. Solution : d) Number of tourists in 2001 = 9 x 2000 = 18 000 Amount spent = 18 000 x 600 = RM 10 800 000 Statistics 113
  • 6. Module PMR114 Exercise 2 : Monday Tuesday Wednesday Thursday Friday Represents 60 bowls The pictogram shows the number of the bowls of noodles sold in a school canteen from Monday to Friday. a) Which day has the highest sales? b) If the profit from each bowl of noodles sold is RM0.20, find the total profit for the five days. c) Find the difference in the profits obtained from the sales on Monday and Friday. Example 3 : Exercise 3: Sales Figures of Watches for Five Shops Sales of Ice Cream for Six Days Day Sale s Figur e s of Watche s for Fiv e Shops Sat 450 400 Fri 350 Numbe r 300 Thurs of 250 watche s 200 Wed 150 100 Tue 50 Mon A B C D E 0 10 20 30 40 50 60 70 80 90 100 110 120 130 Value (RM) Shop Statistics 114
  • 7. Module PMR115 The vertical bar chart given shows the sales figures of watches for five a) On which day did he sell the shops in December. most ice cream? a) What was the difference in number of watches sold between the shops with the highest and the lowest sales? Solution : a) Difference = 450 - 175 b) How much more did he sell on = 275 watches Wednesday compare to Monday? b) If Shop E had an increase in sales of 20% the following month, while Shop A sold 30 fewer watches, what was the total sales for the two shops? Solution : b) Shop E : 120% of 400 = 480 watches c) Calculate his total sales for six days. Shop A : 250 – 30 = 220 watches Total sales for the two shops = 480 + 220 = 700 watches d) If his total profit from his ice cream sales was 15%, calculate c) If the average value of a watch the vendor’s profit on Thursday. was RM150, calculate the total value of the watches sold by all five shops in December. Solution : c) Total number of watches = 250+ 175+ 450+ 325+ 400 = 1600 watches Total value = 1600 x 150 = RM240 000 The horizontal bar chart above shows the sales of an ice cream vendor for six days. Statistics 115
  • 8. Module PMR116 Example 4 : Exercise 4 : M age sh's Best 400 m Time s Numbe r of Employe e s in Ne wTe ch 59 Company from 1999 to 2004 58 57 400 56 55 350 54 300 53 Time (sec) 52 250 Numbe r of 51 employe e s 200 50 150 49 48 100 47 50 46 45 0 1999 2000 2001 2002 2003 2004 1999 2000 2001 2002 2003 2004 Ye ar Ye ar The line graph given shows Magesh’s best times for the 400m The line graph above shows the track event over a period of 6 years. number of employees in NewTech Company from 1999 to 2004. a) From which year onwards did he run below 55 seconds? a) How many employees were there Solution : in 1999? a) From 2001 onwards. b) What was his improvement in time after 6 years of training? b) When was there the greatest Solution : increase in the number of b) Improvement employees ? = Slowest time – Fastest time = 57.5 – 49 c) What was his percentage improvement in time from 2002 to c) How many more employees were 2004? there in 2004 compared to 2001? Solution : Difference in time = 52 - 49 = 3 seconds Percentage improvement in time 3 = × 100 % 52 = 5.77% Statistics 116
  • 9. Module PMR117 Example 5 : Exercise 5 : Total Car Sales in Malaysia in 2003 Others tea 56.3° milk Proton 166.7° Perodua cof f ee chocolate Hy undai All the Form 3 students took part in a 1 survey on their favourite hot drinks. Given that Perodua cars took up The results were shown in the pie 3 chart above. of the nation’s total car sales and Hyundai’s sales was RM21.5 billion. a) Which drink was least preferred by the Form 3 students? a) Find the angle of the sector for i) Perodua cars. Solutions : ii) Hyundai cars. a) Milk was least preferred by Form 3 students. b) Which was the most popular drink among the Form 3 b) How much was the total car sales students? in 2003? Solutions : Tea was the most popular drink among the students. c) How many percent of the c) How much was the sales of students like hot chocolate? Proton cars in 2003? Solutions : b) Percentage of students who like hot chocolate = 90o 360o X 100% = 25% Statistics 117
  • 10. Module PMR118 Example 6: used for represent the price of Mr Song bought a basket of the watermelon. watermelons with RM150. He sold them according to their quantities as d) Find the mean price of the shown in the table below. remaining watermelons, if Mr Price 1.50 2.00 2.50 3.00 Song had only sold 70 fruits with (RM) a collection of RM141. Number 42 12 x 10 of fruits Solution : The total sales for all the d) Number of fruit remaining watermelons was RM207. = 100 -70 = 30 a) Find the value of x. Solution : Mean price of the remaining a) Total sales = 42 x 1.50 + 12 x watermelon : 2.00 + x x 2.50 + 10 x 3.00 207 − 141 207 = 117 +2.5x = 30 2.5 x = 207 – 117 = RM 2.20 x = 90/2.5 = 36 Exercise 6 : b) Find the mean, mode and median of the price of the The table below shows the watermelons. performance of a group of students Solution : in a test. b) Total number of fruits = 42+12+36+10 Scores 6 7 8 9 10 = 100 Frequency 2 4 x 5 2 Total collection Mean = Total number of fruits RM 207 a) Given that the modal score is 8 = and the mean score is greater 100 = RM 2.07 than the mode, find the least Mode = RM1.50 possible value for x. Hence, find its mean.  2.00 + 2.00  Median =   .  2  = RM2.00 c) Among the mean, mode and median, which is suitable to be b) If another 6 students joined the used for representing the price of group and the scores obtained the watermelons? are Solution : 9, 10, 9, 10, 9, 10 c) Mode is not suitable as there are Find the mode, median and 58 fruits costing more than mean of the score. RM1.50. Therefore, mean and median are both suitable to be Common Errors Statistics 118
  • 11. Module PMR119 1. Obtaining information from a pictogram. Group A Group B Represent 50 students Errors Correct Steps Total numbers of students Total numbers of students = 4+6 = ( 4+6) x 50 = 10 = 10 x 50 = 500 2. Error in determining the mode in a frequency table. Marks 0 1 2 3 4 Frequency 3 4 3 1 5 Errors Correct Steps The mode is 3. The mode is 4. The mode is 5. 3. Error in determining the median of a set data. Errors Correct Steps 5, 2, 4, 8, 2, 3, 1 (data not rearrange 1, 2, 2, 3, 4, 5, 8 in order) Median = 3 Median = 8 4. Salary Less than RM1001 to RM1501 to RM2001 to More than RM1000 RM1500 RM2000 RM2500 RM2500 Frequency 14 118 10 5 4 The frequency table above shows the salaries of the staff in Super Home Products Company. Find the number of staff whose salaries are less than RM2000 per month. Errors Correct Steps Number of staff whose salaries are Number of staff whose salaries are less than RM2000 per month less than RM2000 per month = 14 + 118 = 14 + 118 +10 = 132 = 142 5. The combined bar chart shows the sales figures for HIQ Bookstore from January to April. Find the total number of non-fiction books sold. Sales Figures from January to Apri l for HI Q bookstore Month Apr. Mar. Feb. Jan 0 20 40 60 80 100 120 140 Number of books Errors Statistics 119
  • 12. Module PMR121 Total number of non-fiction books Total number of non-fiction books sold sold = 100 + 130 + 100 + 110 = 60 + 80 + 70 + 90 = 440 = 300 Correct Steps 5. The table shows the distribution of the scores obtained in tossing a dice 30 times. Find the mean score of each toss. Score 1 2 3 4 5 6 Frequency 5 4 6 8 3 4 Errors Correct Steps 1+ 2 + 3 + 4 + 5 + 6 Mean Mean = 5+ 4+ 6+8+3+ 4 1(5) + 2(4) + 3(6) + 4(8) + 5(3) + 6(4) = = 0.7 5+ 4+6+8+3+ 4 = 3.4 Extra Exercise 1 Mode : a. 20 g, 50 g, 30 g, 70 g, 50 g, 40 g, 30 g, 60 g, 50 g, 60 g, 50 g, 60 g Mode = _____ g b. 15 mm, 18 mm, 12 mm, 13 mm, 15mm, 17 mm, 12 mm, 16mm, 15 mm, 13 mm, 14 mm, 15 mm Mode = ______ mm c. 4, 5, 6, 2, 1, 4, 6, 7, 5, 6 Mode = d. Number of matches played 1 2 3 4 5 Frequency 1 4 3 2 3 Mode = _______matches e. Height ( cm ) 120 121 122 123 124 Frequency 2 9 7 3 4 Mode = cm Statistics 121
  • 13. Module PMR121 f. Number Of goals 0 1 2 3 4 Frequency 2 5 4 6 4 Mode = goals 2. Median a. 4, 2, 5, 4, 7, 2, 1 c. 2kg, 4kg, 1kg, 5kg, 4kg, 2kg Median = Median = b. 9, 2, 7, 1, 8, 9, 0 d. 30m, 10m, 30m, 10m, 40m Median = Median = e. Number Of goals 0 1 2 3 4 Frequency 1 5 4 4 3 Total frequency = 1 + 5 + 4 + 4 + 3 = Median = Number of goals of the ___ th Frequency = goals f. Grade A B C D E Numbers of students 6 12 9 8 11 Total frequency = 6 + 12 + 9 + 8 + 11 = Median = 3. Mean ; a. 21, 30, 25, 27, 31, 34 b. 7 ,4 , 6 ,8 ,5 ,7 , 5 Mean = Mean = c. Mass (g) 5 6 7 8 Frequency 5 2 6 7 Mean = Statistics 121
  • 14. Module PMR122 4. The pictogram in Diagram below shows the number of durians sold by three fruits sellers. Calculate the total number of durians sold by three of them. Samad Chong Muthu represents 10 durians 5. Sale of chocolate cakes 100 80 60 40 20 0 Days M T W T F S S The line graph shows the sale of chocolate cakes in a week. Find the difference between the highest sales and the lowest sales in the week. 6. 70 60 50 40 30 20 10 0 Day M on Tue s We d Thur Fri The line graph shows the number of cars parked at Jeti Lumut over a period of five days. Each car is charged RM 8 per day. What is the total collection for the five days? 7 2 1 3 4 6 8 8 7 5 4 5 4 3 1 2 1 1 4 2 4 The data shows the scores obtained by 20 pupils in a game. a) By using the data given, complete the following table. Score 1 2 3 4 5 6 7 8 Frequency b) State the mode Statistics 122
  • 15. Module PMR123 8. The mean of 5, y, 2y, 3y, 12,12, 15, 20 is 11. Find the value of y. 9. Calculate the difference between mean and median of the numbers 5, 11, 20, 23, 15, 9, 3, 18. 10. Find the difference between mode and median of the numbers 4, 3, 5, 9, 9, 9, 3, 7, 9. 11. Given that the mean of 3, 5, 10, 2, x, 15, y is 8, find the value of x+y. 12. The pie chart shows the number of coloured balls in a store. Green 8 Purple White 12 6 10 Black Calculate the angle of the sector which represents black balls. 13. Diagram below is a line graph which shows the number of residents in a town from 1997 to 2004. a) During which year did the number of residents increase the most? b) How many residents were there in the town at the beginning of 2001? c) Calculate the percentage increase of residents during the year 2002. Statistics 123
  • 16. Module PMR124 Questions based on PMR Format 1. The pictogram below shows the number of cars sold by Syarikat Maju Jaya from year 2004 to 2007. 2004 2005 2006 2007 Represents 50 cars. a) Number of cars sold in year 2006 = ______________ b) If 200 cars were sold in year 2005, complete the pictogram above. 2. The frequency table below shows the marks obtained by 40 students from form 3 Budiman in the first round of a mathematics quiz. Score 1 2 3 4 5 6 Number of 3 8 5 12 7 5 students a) If students who get more than four marks will go on to the next round, how many students never made to the second round? b) Calculate the percentage of student that can go to the second round. Statistics 124
  • 17. Module PMR125 3. The pie chart below shows the favourite colours chosen by a group of car owners. Tomato Re d 12 Golde n Ye llow 24 Lime Gre e n 8 Sky b lue 16 a) Find the angle of sector for cars with Golden Yellow colour. b) Calculate the percentage of cars with Tomato Red colour. 4. The bar chart below shows number of books read by form one, form two and form three students in SMK Sinar Mutiara for the past two months. Nu m b er of books Nilam 2008 35 30 25 20 Sain s 15 English 10 5 0 1 2 3 For m a) Base on the bar chart above, complete the table below. Form 1 2 3 Number of books b) Find the difference between Science and English books read by all students. Statistics 125
  • 18. Module PMR126 5. 21 , 13, 16, 19, 11, 16, 16 Base on the data above, determine: a) the mode b) the median 6. The bar chart below shows the population of Kampung Selangkah, Kampung Temai, Kampung Dusun and Kampung Air. Number of resident 400 300 200 m ale fe m ale 100 0 Kam pung Kam pung Kam pung Kam pu ng Se langk ah Te m ai Du sun Air a) Find the total number of male in all the four Kampung. b) Find the percentage of female to the whole population? Statistics 126
  • 19. Module PMR127 7. Class Raden Mayang Bahagia Adil Jujur Iklas Collection(RM) 200 300 50 250 100 310 Based on the table above, complete the bar charts below. (RM) CLASS FUND 350 300 250 200 150 100 50 0 CLASS Rad en Mayan g Bahagia Adil Jujur Iklas 8. Number of points 10 20 30 40 50 60 Number of students 5 4 7 5 6 3 The frequency table above shows the marks obtained by a group of students in a marching competition. a) Find the number of students involved in the event. b) Find the mean point from the table. Statistics 127
  • 20. Module PMR128 9. 2001 2002 2003 2004 2005 Represents 25 computers a) The pictograph above shows the sale of computers by Syarikat Indah Computer in five years . Complete the pictograph if the number of computers sold in year 2003 were 100 sets. b) Find the total number of computers sold in five years. 10. Number of books 1 2 3 4 5 6 Number of students 2 5 8 3 6 7 The frequency table above shows the number of books read by students in form 3 Bahagia of SMK Pekan under “ PROJEK NILAM”. a) Find the number of students involved in “PROJEK NILAM”. b) Determine the mode. Statistics 128
  • 21. Module PMR129 11. The following data shows the marks obtained by pupils in a mathematic test: 23 27 26 27 22 22 22 23 26 25 24 23 27 27 26 23 22 22 25 25 22 27 26 26 26 25 24 24 23 22 Marks 22 23 24 25 26 27 Frequency a) Complete the frequency table above based on the data given b) Find the mode 12. 21, 26, 29, 27, 21, 25, 25, 26, 29, 28, 30, 33, 23,29 a) Find the mode b) Find the median 13. The table below shows the marks obtained in an English test. Marks 10 20 30 40 50 Frequency 4 X 15 11 7 a) Given that the number of frequency is 50, find the value of X b) Determine the mode. Statistics 129
  • 22. Module PMR130 14. The Pie chart below shows the subjects most liked by a group of 36 students. Science Geography 120.0º 60.0° History 130.0° Mathematics a) Find the number of students who like science . b) Find the percentage of pupils who like history. 15. The horizontal bar chart below shows the number of vehicles sold by three companies A, B and C. CAR VAN C op y Cm a n B A 0 20 40 60 80 No. of ve hicle s Number of Vehicles a). Calculate the number of vehicles sold by companies A and C. b). Calculate the difference between the number of vans sold by companies B and C. Statistics 130
  • 23. Module PMR131 16. Diagram below is a line graph which shows the number of residents in village X and village Y from 1998 to 2004. Y X a) In which year the difference in the number of residents between village X and village Y is 1 500? b) How many residents are there in village Y in the year 2002? c) Calculate the percentage increase in the number of residents in village X from 2000 to 2002. Statistics 131
  • 24. Module PMR132 PMR past year questions 2004 1. The data in Diagram 5 shows marks obtained by 20 participants in a quiz. 1 4 6 5 4 6 3 5 4 6 2 1 2 4 6 1 2 4 2 3 a) Using the data, complete the frequency table in the answer space. b) State the mode. [3 marks] Answer : a) Marks 1 2 3 4 5 6 Frequency b) 2. Table 1 shows the number of books in the reading corners of three classes. Class Number of Books Aman 75 Bestari 60 Cerdas 90 Table 1 The information for Bestari class is shown fully in the pictograph in the answer space. Complete the pictograph to represent all the information in Table 1. [3 marks] Answer : Number of books in the reading corners Aman Bestari Cerdas Represents _______ books Statistics 132
  • 25. Module PMR133 2005 3. Table 1 shows the number of students who play four types of games. Types of games Number of students Ping-pong 8 Badminton 15 Hockey 25 Handball 12 Table 1 The information for badminton is shown fully in the pie chart in the answer space. Complete the pie chart to represent all the information in Table 1. [5 marks] Answer : Badminton 90 ° Statistics 133
  • 26. Module PMR134 2006 4. Table 1 shows the profit made from the sales of nasi lemak at a stall over 5 days. Day Monday Tuesday Wednesday Thursday Friday Profit (RM) 32 40 24 28 28 Table 1 On Diagram 4 in the answer space, draw a line graph to represent all the information in Table 1. Use the scale 2 cm to RM8 on the vertical axis. [5 marks] Answer : Profit (RM ) 40 32 24 16 8 Day Mon Tu e We d Th ur Fr i Diagram 4 Statistics 134
  • 27. Module PMR135 5. Diagram 5 is a pie chart which shows the number of pupils in five group who complete an assignment during a motivational camp. Tuah 10 Jebat x Lekiu Diagram 5 12 Kasturi Lekir 2x 8 It is given that the total number of pupils who complete the assignment is 36. a) Find the value of x. b) Calculate the angle of the sector representing the Tuah group. Show your working. c) State the mode of your data. [5 marks] Answer : a) b) c) 2007 6. Table 1 shows three activities participated by a group of 50 students. Activities Number of students Chess 24 Hockey M Choir 18 Table 1 a) Find the value of M b) Hence , represent all the data by drawing a bar chart in the answer space. [4 marks] Answer : a) Statistics 135
  • 28. Module PMR136 b) Numbe r of stude nts 28 24 20 16 12 8 4 0 Activ itie s Cheess Hockey Choir 7. Diagram 3 shows the scores obtained by 15 Police Cadets in a shooting competition. 1, 2, 4, 3, 1, 2, 4, 1, 3, 2, 1, 3, 1, 1, 3 Diagram 3 a) Using the data, complete the frequency table in the answer space. b) State the median. [ 3 marks] Statistics 136
  • 29. Module PMR137 Answer : a) Score Frequency 1 2 3 4 b) Median = 2008 8. Table 15 in the answer space shows the number of gold medals obtained by four schools in a sports competition. The information for school L is shown fully in the pie chart in Diagram 15. Complete a) the angles of the sectors for school M and school N in Table 15. b) the pie chart in Diagram 15 to represent all the information in Table 15. [5 marks] Answer: a) School Number of gold Angle of sector medals K 10 300 L 60 180o M 20 N 30 b) L 180o Diagram 15 Statistics 137
  • 30. Module PMR138 CHAPTER 8 : STATISTICS ANSWERS Exercise 1 1f. 3 a. 11 b. 34 2a. 4 c. Grade C 2b. 7 2c. 3 Exercise 2 2d. 30m a. Monday 2e. 17, 9 , 2 b. RM288 2f. 46, C c. RM24 3a. 28 Exercise 3 3b. 6 a. Saturday 3c. 6.75 b. RM 45 c. RM 530 4. 120 d. RM11.25 5. 80 Exercise 4 a. 25 6. RM2000 b. between 2003 and 2004 c. 275 7a. Exercise 5 Score 1 2 3 4 5 6 7 8 ai. 120o Frequency 4 3 2 5 2 1 1 2 aii. 17o 7b. 4 b. RM 455.30 c. RM 210.80 8. 4 Exercise 6. 9. 0 a. x= 6 mean= 8.05 10. 2 b. mode = 9 median = 9 11. 21 mean = 8.4 12. 100o Extra Exercise 1a. 50 13a. 1997 and 2000 1b. 15 13b. 28500 1c. 6 1 1d. 2 13c. 9 11 1e. 121 Statistics 138
  • 31. Module PMR139 Questions based on PMR Format 1. a) 250 9. a) Draw 2 symbols correctly b) 4 symbols drawn b) 500 computers 2. a) 28 students 10. a) 31 b) 30% b) 3 3. a) 144º 11. a) 7, 5 ,3, 4, 6, 5 b) 20% b) 22 4. a) 45, 35, 45 12. a) 29 b) 15 b) 26.5 5. a) 16 13. a) 13 b) 16 b) 30 6. a) 650 14. a) 12 students b) 43.48 b) 13.9% 7. Draw the bars representing 15. a) 200 Mayang, Adil and Jujur correctly b) 10 8. a) 30 16. a) year 2001 b) 34 b) 4750 c) 60% PMR Past Year Questions 1. a) Marks 1 2 3 4 5 6 Frequency 3 4 2 5 2 4 b) 4 2. Number of books in the reading corners Aman Bestari Cerdas Represents ___30____ books Statistics 139
  • 32. Module PMR140 3. Ping Pong Badminton c1 48 ° 90 ° 150° 72 ° Hockey Hand ball 4. Profit (RM ) 40 32 24 16 8 Day Mo n Tu e We d Th ur Fr i Diagram 4 5. a) 2 b) 100o c) Lekiu Statistics 140
  • 33. Module PMR141 6. a) 8 6. b) Numbe r of stude nts 28 24 20 16 12 8 4 0 Activ itie s Cheess Hockey Choir 7. a) Score Frequency 1 6 2 3 3 4 4 2 b) 2 8. a) a) Number of gold School Angle of sector medals K 10 300 L 60 180o M 20 600 N 30 900 b) K 30 ° M ° 60° L ° 180° ° 90° N Statistics 141