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