Grouping and Displaying Data to Convey Meaning: Tables & Graphs chapter_2 _from_Statistics For Management

Product Categories Per Customer at the PB Store

September 11, 2001, attack on the World
Trade Center in New York City and the
Pentagon in Washington D.C.
A Sad Day

Grouping and Displaying Data to Convey
Meaning:
Tables and Graphs
By
Prof. P. N. Borkar
(Asst. Prof. GHRCE, Nagpur)

Some Definitions
 Data: are collections of any number of
related observations.
 Data set: Collection of data.
 Data point: single observation.

Raw Data
Arranging Data using Data Array &
Frequency Distribution
Constructing a Frequency Distribution
Graphing Frequency Distributions
How can we Arrange Data?

Raw Data
Constructing a Frequency Distribution

 Aim: logical conclusion
 Our observations must be organized so
that we can pick out patterns
Collecting Data:
 Data came from actual observations or
from records.
 Computer programmers says ‘GIGO’

…
Test the data by asking questions:
 Where did the data come from?
 Do the data support or contradict other
evidence?
 Is evidence missing?
 How many observations do we have?
 Is the conclusion logical?

…
Difference between Samples & Populations
 Population is a whole
 Sample is fraction or segment of that
whole
 Information from sample makes inference
about the population.
 Ex. Poll of 2500 Indians to predict all adults living in
India.

…
Advantages of samples,
 Studying samples is easier
 It costs less
 Takes less time
 Reduces risk
‘A representative sample contains relevant
characteristics of population in the same
proportion as they are included in that population’

Exercise 1:
Is this conclusion drawn from sample or
population
Q. 25% of cars sold in India in 2013 were
manufactured in Japan.
Ans: Population
Reason: our department of commerce
keeps statistics of all the cars sold in India

Raw Data
 Information before it is arranged &
analyzed is called raw data.
H.S CLG H.S CLG H.S CLG H.S CLG
3.6 2.5 3.5 3.6 3.4 3.6 2.2 2.8
2.6 2.7 3.5 3.8 2.9 3.0 3.4 3.4
2.7 2.2 2.2 3.5 3.9 4.0 3.6 3.0
3.7 3.2 3.9 3.7 3.2 3.5 2.6 1.9
4.0 3.8 4.0 3.9 3.1 2.5 2.4 3.2
Problem
facing
admission
staff
Data are not necessarily information.
Goal: Summarize and present data in useful ways to
support prompt and effective decisions.

Exercise II:
Look table of HS & CLG grades
Q. Why do these data need further
processing? Can you form any
conclusion?
Ans: we can not draw any conclusion form
it.
Need to: do certain amount of rearranging.
(ex. Listing, grades from highest to lowest,

Arranging Data using Data Array
& Frequency Distribution
 Data Array: arranges values in ascending
or descending order.
16.
2
15.
8
15.
8
15.
8
16.
3
15.
6
15.
7
16.
0
16.
2
16.
1
16.
8
16.
0
16.
4
15.
2
15.
9
15.
9
15.
9
16.
8
15.
4
15.
7
15.
9
16.
0
16.
3
16.
0
16.
4
16.
6
15.
6
15.
6
16.
9
16.
3
Ex. Sample of Daily production in yards of 30 carpet looms
15.
2
15.
7
15.
9
16.
0
16.
2
16.
4
15.
4
15.
7
15.
9
16.
0
16.
3
16.
6
15.
6
15.
8
15.
9
16.
0
16.
3
16.
8
15. 15. 15. 16. 16. 16.
Data Array

… a better way
The Frequency Distribution:
Is a table that organizes data into classes
Ex. Data Array of average inventory (in days)
2.0 3.8 4.1 4.7 5.5
3.4 4.0 4.2 4.8 5.5
3.4 4.1 4.3 4.9 5.5
3.8 4.1 4.7 4.9 5.5
Class Frequency
2.0 to 2.5 1
2.6 to 3.1 0
3.2 to 3.7 2
3.8 to 4.3 8
4.4 to 4.9 5
5.0 to 5.5 4
Frequency
Distribution
Note: we lose some information in constructing frequency distribution,
yet it offers new insights into patterns of data.

…
Relative Frequency Distribution:
- It express the frequency of each value
as a fraction or a percentage of total
number of observations.
Class Frequency Relative
Frequency
2.0 to 2.5 1 0.05
2.6 to 3.1 0 0.00
3.2 to 3.7 2 0.10
3.8 to 4.3 8 0.40
4.4 to 4.9 5 0.25
5.0 to 5.5 4 0.20
20 1.00

Exercise III:
Data array and frequency distribution
823 648 321 634 752
669 427 555 904 586
722 360 468 847 641
217 588 349 308 766
Company: PB Transmission Fix-It
Number of service tickets submitted by 20 stores
Q. How many stores are not breaking even and how many are to get bonus
?
Not breaking even < 475
To get bonus > 725
217 360 586 648 766
308 427 588 669 823
321 468 634 722 847
349 555 641 752 904
Not breaking even : 7
To get bonus : 5

…
4.3 2.7 3.8 2.2 3.4
3.1 4.5 2.6 5.5 3.2
6.6 2.0 4.4 2.1 3.3
6.3 6.7 5.9 4.1 3.7
Company: PB Transmission Fix-It
Number of hrs taken by mechanics to remove, repair and replace
transmissions
Q. Construct frequency distribution with intervals of 1.0 hrs ? What
conclusions can you reach about productivity of mechanics ? If more
than 6.0 hrs is evidence of unsatisfactory performance, does it have
major or minor problem with particular store?
Class 2.0 to 2.9 3.0 to 3.9 4.0 to 4.9 5.0 to 4.9 5.0 to 6.9
Frequenc
y
5 6 4 2 3
2 2.7 3.4 4.3 5.9
2.1 3.1 3.7 4.4 6.3
2.2 3.2 3.8 4.5 6.6
2.6 3.3 4.1 5.5 6.7
There is only 15 % takes more than 6 hrs, it is minor productivity
problem

Raw Data
Constructing a Frequency
Distribution

Constructing a Frequency
Distribution
16.
2
15.
8
15.
8
15.
8
16.
3
15.
6
15.
7
16.
0
16.
2
16.
1
16.
8
16.
0
16.
4
15.
2
15.
9
15.
9
15.
9
16.
8
15.
4
15.
7
15.
9
16.
0
16.
3
16.
0
16.
4
16.
6
15.
6
15.
6
16.
9
16.
3
Ex. Sample of Daily production in yards of 30 carpet looms
Step 1: Decide on the type and number of classes for dividing the data
Need to consider Attributes, here we have considered yards produced.
How many number of classes ?
What will be the range of each class ?

…
Class in
Yards
Frequency
15.1 to
15.5
2
15.6 to
16.0
16
16.1 to
16.5
8
16.6 to
17.0
4
30
Class in Yards Width Frequency
15.1 to 15.5 0.5 2
15.6 to 15.8 0.3 8
15.9 to 16.1 0.3 9
16.2 to 16.5 0.4 7
16.6 to 16.9 0.4 4
30
Equal Width Unequal Width
Problem with unequal width: distribution is much more difficult to interpret.

…
So we need to make the class intervals of equal size,
Width of
class interval
=
Next unit value
after largest value
Smallest value in
the data-
Total Number of
class intervals
= (17.0 – 15.2)/ 6
= 0.3 Yards

…
Step 1I: Sort the data points into classes and count the number of points
in each class
Class in Yards Frequenc
y
15.2 to 15.4 2
15.5 to 15.7 5
15.8 to 16.0 11
16.1 to 16.3 6
16.4 to 16.6 3
16.7 to 16.9 3
30
15.
2
15.
7
15.
9
16.
0
16.
2
16.
4
15.
4
15.
7
15.
9
16.
0
16.
3
16.
6
15.
6
15.
8
15.
9
16.
0
16.
3
16.
8
15.
6
15.
8
15.
9
16.
1
16.
3
16.
8
15.
6
15.
8
16.
0
16.
2
16.
4
16.
9

…
Step III: Illustrate the data in a chart
looms<-c(16.2, 15.7, 16.4, 15.4, 16.4, 15.8, 16.0, 15.2, 15.7, 16.6, 15.8, 16.2, 15.9, 15.9, 15.6,
15.8, 16.1, 15.9, 16.0, 15.6, 16.3, 16.8, 15.9, 16.3, 16.9, 15.6, 16.0, 16.8, 16.0, 16.3)
breaks=seq(15.1, 17.0, 0.4)
cbind(table(cut(looms, breaks)))
hist(looms, breaks="Sturges")

Exercise IV:
Here are the ages of 30 people who bought video recorder @ PB Music
Shop
26 37 40 18 14 45 32 68 31 37
20 32 15 27 46 44 62 58 30 42
22 26 44 41 34 55 50 63 29 22
Q. Looking data just as they are, what conclusions can you come to
quickly about PB Music shop?
Ans: It is difficult to tell anything from raw data

…
Q. Construct a 6 category closed classification. Does having this
enable you to conclude anything more about PB Music shop ?
Class 10-19 20-29 30-39 40-49 50-59 60-69
Frequenc
y
3 7 7 7 3 3
Most video recorders are bought by people between 20 to 50, so
marketing effort should be aimed at that group

Graphing Frequency
Distributions
Graph gives data in two-dimensional picture.
Horizontal Axis: values of variable
Vertical Axis: frequencies of the classes
Histograms:
Is series of rectangles, each proportional in range of
values and proportional in number of items falling in it.

…
Frequency Polygons
I: mark frequencies on vertical axis and values of
variables on horizontal axis
II: plot each class frequency by drawing dot above its
midpoint, and connect the successive dots with straight
lines

…
Why do we need both?
Histogram
1. Rectangle clearly shows each separate class in the
distribution.
2. The area of rectangle, shows proportion of the total
number of observations that occur in class.
Frequency Polygon
1. It is simpler
2. It sketches outline of the data pattern more clearly
3. Polygon becomes smooth and curvelike as we
increase the number of classes and the number of

…
Ogives
 Is a graph of cumulative frequency distribution.
 It enables us to see how many observations lie above
or below certain values.

Exercise IV:
Ganga River:
River flow Frequenc
y
1001-1050 7
1051-1100 21
1101-1150 32
1151-1200 49
1201-1250 58
1251-1300 41
1301-1350 27
1351-1400 11
Total 246
Q.1: Create More than Ogive
River flow
>
Frequency Cumulative
frequency
1000 7 246
1050 21 246-7=239
1100 32 239-21=218
1150 49 218-32=186
1200 58 186-49=137
1250 41 137-58=79
1300 27 79-41=38
1350 11 38-27=11
1400 0 11-11=0

PB Store
Product Categories
At the Miami, Florida, airport, officials each
week select a random sample of
passengers. For each person selected, the
time spent in the security screening line is
recorded. The waiting times (already
sorted from high to low), in seconds, for
one such sample of 72 passengers are as
follows:

Grouping and Displaying Data to Convey Meaning: Tables & Graphs chapter_2 _from_Statistics For Management

Grouping and Displaying Data to Convey Meaning: Tables & Graphs chapter_2 _from_Statistics For Management

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Grouping and Displaying Data to Convey Meaning: Tables & Graphs chapter_2 _from_Statistics For Management