Diagrammatic and graphical representation of data

Managerial Statistics-Diagrammatic and graphical representation of data

1. GOA INSTITUTE OF
MANAGEMENT



SUBJECT: MANAGERIAL STATISTICS
ASSIGNMENT ON
DIAGRAMMATIC AND GRAPHICAL
REPRESENTATION OF DATA









SUBMITTED TO :- SUBMITTED BY:-
Prof. ROHIT MUTKEKAR RACHNA GUPTA
Roll No. 2020046
PGP1 SECTION-A
SESSION- 2020-22

2. Diagrammatic and Graphical Representation of
Data

MEANING OF GRAPHICAL REPRESENTATION OF
DATA

 A graphical representation is the geometrical image of a set of
data.
 It enables to think about a statistical problem in visual terms.
 It is an effective and economic device for the presentation,
understanding and interpretation of the collected data.
 Helps in comparison of data.

TYPES OF GRAPHICAL REPRESENTATION






•Frequency Distribution
•Bar Chart
•Pie Chart
•Pareto Daigram
Catagorical
Varibles
•Line chart
•Scatter Plot
•Ogives
•Histogram
•Frequency Curve
Numerical
Variables

3. PERCENTAGE BAR DAIGRAM

 In bar graphs data is represented by bars.
 The bars can be made in any direction i.e. Vertical or Horizontal.
 The bars start from a common horizontal or vertical line and their length
indicates the corresponding values of statistical data.

WHEN TO USE BAR CHART?
Bar chart is used when we have to compare between categories of data
and the change in data is large.

EXAMPLE 1-

Prepare Percentage Bar Chart for the following data.
YEAR SALES
(Rs)
GROSS
PROFIT(Rs)
NET
PROFIT(Rs)
2000 100 30 10
2001 120 40 15
2002 130 45 25
2003 150 50 25
The steps to plot a chart are as follows:
 In order to prepare the percentage bar diagram, we need to convert values of
each category into Percentage.
Using formula percentage= (ACTUAL VALUE / TOTAL OF ACTUAL VALUE) *100
Now we can make a new table having percentage values of each category.
 Draw vertical and horizontal line and label them as X-Axis and Y-Axis.
 Label the Horizontal axis as Amount in Percentage and Vertical axis as Years.
 Select Clustered Bar from the Chart Tab.
 Looking the data we have to decide the numbering on the axis.
 Plot the graph


YEAR SALES (Rs) GOSS
PROFIT(Rs)
NET PROFIT
(Rs)
2000 71.43 21.43

7.14
2001 68.57 22.86 8.57
2002 65 22.5 12.5
2003 66.67 22.22 11.11

4. INTERPRETATION
The above chart represents the percentage Sales, Gross Profit and Net Profit of 4years.
 Maximum and minimum sales incurred in 2000 and 2002 respectively.
 Maximum and minimum gross profit incurred in 2001 and 2000 respectively.
 Maximum and minimum net profit incurred in 2002 and 2000 respectively.

EXAMPLE 2:
The cropping pattern of Tamil Nadu in 2 different years was as follows
CROPS AREA
2009 2010
CEREALS 3600 3650
OILSEEDS 1000 1150
PULSES 400 450
COTTON

200 230
OTHERS 800 820


In order to prepare the percentage bar diagram, we need to convert values of each
category into Percentage.
0 10 20 30 40 50 60 70 80
2000
2001
2002
2003
AMOUNT IN PERCENTAGE
YEARS
Percentage Bar Diagram
NET PROFIT(Rs) GROSS PROFIT(Rs) SALES(Rs)

5. Using formula percentage= (ACTUAL VALUE / TOTAL OF ACTUAL VALUE) *100

Now we can make a new table having percentage values of each category.

CROPS AREA
2009 2010
CEREALS 49.65 50.34
OILSEEDS 46.51 53.49
PULSES 47 52.94
COTTON

46.51 53.49
OTHERS 49.38 50.62


INTERPRETATION
 It is a Stacked Bar Chart representing percentage area of 6 CROPS in the State
of TAMIL NADU in 2009 and 2010.
 In 2019 the highest and lowest percentage area is of Cereals and Oilseeds &
Cotton respectively.
 In 2010 the highest and lowest percentage area is of Cotton
 & Oilseeds and Cereals respectively.
0% 20% 40% 60% 80% 100%
CEREALS
OILSEEDS
PULSES
COTTON
OTHERS
PERCENTAGE AREA
CROPS
PERCENTAGE STACK BAR CHART
2009 2010

6. MULTIPLE BAR CHART

 Sometimes there are more than two sets of data to be compared in a bar
chart. In that case, a multiple bar chart can be used.
 A multiple bar chart compares as many data sets you want.
EXAMPLE 1:
A farmer takes his produce to the market each weekend. The farmer keeps track
of the amount of produce he sells each day from each vegetable.
Here is data from the weekend:
TYPE OF VEGETABLE POUNDS SOLD (LBS)
DAY ONE DAY TWO DAY THREE
SQUASH 32 36 36
ZUCCHINI 40 33 37
CORN 56 65 67
CARROTA 28 25 23
LETTUCE 27 31 34
TOMATOES 44 54 58

Steps to plot multiple bar:
 Draw vertical and horizontal line and label them as X-Axis and Y-Axis.
 Label the Horizontal axis as Type of Vegetables and Vertical axis as Pounds
Sold(lbs) .
 On horizontal axis name the vegetables at some distance
 Select Column Bar from the Chart Tab.
 Looking the data, we have to decide the numbering on the Y-axis.
 Plot the graph

7. INTERPRETATION
 It is observed that CORN is sold the most among all the vegetables in all the 3
days.
 Highest amount of pound sold In corn is observed on 3
rd
day.
 We can also observe the individual sale in 3 days of different vegetables.
 This chart will help the farmer to decide when he should produce more or less.
For example- one day 1 farmer should produce more corn and least lettuce to
sell.
 We can also determine which is the most popular and least popular vegetable.
EXAMPLE 2:
The following table shows the sale of ice cream in the months of July, August,
September and October in respective 4 weeks.
WEEK JULY AUGUST SEPTEMBER OCTOBER
WEEK 1 500 800 600 400
WEEK 2 800 900 500 200
WEEK 3 700 600 400 100
WEEK 4 900 800 300 100
0
10
20
30
40
50
60
70
80
SQUASH ZUCCHINI CORN CARROT LETTUCE TOMATOES
POUNDS
VEGETABLES
MULTIPLE BAR CHART
DAY1 DAY2 DAY3

8. INTERPRETATION
 It is observed from this chart that the highest sale of ice-cream is in the 4th week
in the month of July and 2
nd
week in the month of August.
 Minimum sale is recorded in the3rd and 4
th
week of October .


SCATTER PLOT
 Use to study correlation between two random variables.
 Studying the pattern formed by the points we can determine the relation
between two variables which cannot be seen by just looking at the data.
 Relation can be – Positive, Negative or No correlation
EXAMPLE 1:
Plot the data to show relation between TIME SPEND ON WATCHING TV Vs TIME SPEND
ON HOME WORK.
WORKING:
 Collect data for time spend on tv and homework.
 Draw vertical and horizontal axis.
 Name horizontal axis as TIME SPEND ON TV and vertical axis as TIME SPEND ON
HOMEWORK
 Plot data on the graph in form of dots.
500
800
700
900
800
900
600
800
600
500
400
300
400
200
100 100
WEEK1 WEEK2 WEEK3 WEEK4
NUMBER OF SALE
WEEK
MULTIPLE BAR CHART
JULY AUGUST SEPTEMBER OCTOBER

9. TV
(MIN)
HOMEWORK
(MIN)
25 200
30 180
50 150
120 100
200 45
220 30

INTERPRETATION
 As time on tv is increasing, time on homework appears to be decreasing.
 This shows a NEGATIVE CORRELATION between the two variables.

EXAMPLE 2:
Plot data to show relationship between person’s weight and height of age 20-30
years.




WEIGHT
(KG)
HEIGHT
(IN CM)
50 170
55 180
65 172
80 162
100 135
125 136
200 130
0
50
100
150
200
250
0 50 100 150 200 250
TIME ON HOMEWOK
TIME ON TV
SCATTER CHART
50, 170
55, 180
65, 172
80, 162
100, 135125, 136
200, 130
0
20
40
60
80
100
120
140
160
180
200
0 50 100 150 200 250
HEIGHT
WEIGHT
SCATTER CHART

10. INTERPRETATION
 Initially there was a negative correlation between the two variables but later on
the correlation is constant.
 We can conclude that people of weight between 50-80 has height between
170-160 whereas weight more than 100 kg results in less height.
BOX PLOT
A box plot gives a graphic presentation of data using 5 measure:
 The median (centre element of the data set)
 The first and third quartile (middle values of the first half and second half of the
data set after finding median)
 The smallest and the largest values.
 It is also called BOX-AND-WISHKER PLOT.

EXAMPLE 1:
Plot the following numbers on Box plot –

22,2,3,4,9,10,2,7,20,8,8,10,1

Steps to plot:

 First write the numbers in order – 1,2,2,3,4,7,8,8,9,10,10,20,22
 Find the minimum and maximum value.
Minimum value= 1
Maximum value= 22
 Find the median- since there are odd number of elements => [(N+1)/2]th
value = 7
th
value of data array.
Median = 8
1,2,2,3,4,7,8,8,9,10,10,20,22
 Find the first quartile.
1,2,2,3,4,7
Q1= [(N+1)/2]th value = 3.5
th
value
Q1= 2.5
 Find the third quartile.
8,9,10,10,20,22
Q3= [(N+1)/2]th value = 3.5
th
value
Q3= 10

PLOT THE FOLLOWING VALUES IN THIS SEQUENCE ON EXCEL SHEET
MINIMUM VALUE= 1
QUARTILE 1= 2.5
MEDIAN = 8
QUARTILE 3= 10
MAXIMUM VALUE= 22

11. EXAMPLE 2 :
Plot the even number of data elements on Box Plot

30,33,45,45,50,78,80,12,12,20,30,32

Solution:
 Arranged data:
12,12,20,30,30,32,33,45,45,50,78,80
 Maximum value= 80
 Minimum value= 12
 Median = (12+1)/2 = 6.5
th
value
= 32.5
 Quartile1 = 12,12,20,30,30,32
= (20+30)/2
= 25
 Quartile 3= 33,45,45,50,78,80
=(45+50)/2
= 47.5

12. HISTOGRAM CHART
 Graphical representation of the frequency distribution of data in form of bar is
called Histogram.
 Helps to easily evaluate continuous data.
Steps to plot Histogram
 Collect raw discrete data
 Calculate range
 Determine number of intervals
 Calculate width of each intervals
 Write all the class intervals
 Count number of data points in each interval
 Prepare tally sheet
 Plot histogram.


EXAMPLE 1:

These are the waiting times(minutes) spent by 20 customers in a Bank office for
availing Locker facility.

43.1,35.6,37.6,36.5,45.3,43.5,40.3,50.2,47.3,31.2,42.2,45.5,30.3,31.4,35.6,45.2,54.1,45.6,3
6.5,
43.1

13. SOLUTION:
Range= maximum value – minimum value
= 54.1- 30.3
=23.8
To determine number of intervals we are using Sturges Formula
n= 1+3.322log10N
= 1+3.22log10 20
= 5.18
=6

Width of each interval= Range/n
= 23.8/6
=3.967
=4

CLASS INTERVAL
(in min)
CUSTOMERS
30.3 – 34.3 3
34.3-38.4 5
a38.4-42.5 2
42.5-46.3 7
46.3-50.4 2
50.4-54.5 1

14. EXAMPLE 2:
Heights (in cm) of the (20) students of PGP1 are given as:
120,155,133,128,155,180,140,144,146,167,178,155,150,160,181,162,139,145,175,135.
Draw histogram for this data.
CLASS-
INTERVALS
NUMBER
OF
STUDENTS
120-131 2
131-142 4
142-153 4
153-164 5
164-175 2
175-186 3


FREQUENCY CURVES

 FREQUENCY CURVE is the presentation of frequency distribution by a smooth
curve

15.  The only difference between frequency polygon and frequency curve is that,
frequency polygon is made from straight line whereas frequency curve is made
of smooth lines.
EXAMPLE 1:
Plot the frequency curve for the following data
Marks obtained by 20 students of PGP1 in MANAGERIAL STATISTICS Subject out of
100.
80,85,35,46,80,82,90,50,62,75,20,35,67,90,45,43,87,54,67,43.
Steps to plot Frequency Curve
 Collect raw discrete data
 Calculate range
 Determine number of intervals
 Calculate width of each intervals
 Write all the class intervals
 Count number of data points in each interval/ frequency
 Prepare tally sheet
 Plot frequency curve


Range= maximum - minimum value.
=90-20
=70
Number of class intervals = 1+3.322log10N
n = 5.18
n = 6
Width of each interval = Range/n
= 11.6
= 12

CLASS INTERVALS
(MAKRS
OBTAINED)
FREQUENCY
(NUMBER OF
STUDENTS)
20-32 (1) 1
32-44(2) 4
44-56(3) 4
56-68(4) 3
68-80(5) 2
80-92(6) 6

16. EXAMPLE 2:
Draw frequency curve for the following data
SEEDYEILDS NUMBEROF
PLANTS
2.5-3.5

4
3.5-4.5

6
4.5-5.5 10
5.5-6.5 26
6.5-7.5 24
7.5-8.5 15
8.5-9.5 10
9.5-10.5 5

0
1
2
3
4
5
6
7
0 1 2 3 4 5 6 7
FREUENCY
CLASS INTERVALS
FREQUENCY CURVE

17. OGIVES
 It is also known as CUMULATIVE FREQUENCY POLYGON
 It is similar to frequency polygon just the difference is it shows Cumulative
frequencies-less than and more cumulative frequencies.
EXAMPLE 1:
Draw ogives for the following data
Class
Interval
Frequency
0-10 4
10-20 7
20-30 6
30-40 10
40-50 2

Steps to draw ogive
 Calculate less than cumulative frequency by adding frequencies from top to
bottom.
 Calculate more than cumulative frequency by adding frequencies from
bottom to top.
 Plot frequency polygon for both the frequencies.


0
5
10
15
20
25
30
0 2 4 6 8 10 12
NUMBER OF PLANTS
SEED YEILD
FREQUENCY CHART

18. CLASS
INTERVALS
FREQUENCY <CUMULATIVE
FREQUENCY
>CUMULATIVE
FREQUENCY
0-10 4 4 29
10-20 7 11 25
20-30 6 17 18
30-40 10 27 12
40-50 2 29 2



EXAMPLE 2:
Draw ogives chart for the following data
GRAIN YEILD NUMBER OF PLANTS
65-85 3
85-105

5
105-125 7
125-145 20
145-165 24
165-185 26
185-205 12
205-225 2
225-245 1

4
11
17
27
2929
25
18
12
2
0
5
10
15
20
25
30
35
10 20 30 40 50
FREQUENCY
CLASS INTERVAL
Chart Title

19. SOLUTION:






















3
8
15
35
59
85
97
2 1
100
97
92
85
65
41
15
3 1
65-8585-105105-125125-145145-165165-185185-205205-225225-245
FREQUENCY
GRAIN YEILD
Chart Title
GRAIN
YEILD
NUMBER
OF PLANTS
<CUMULATIVE
FREQUENCY
>CUMULATIVE
FREQUENCY
65-85 3 3 100
85-105

5 8 97
105-125 7 15 92
125-145 20 35 85
145-165 24 59 65
165-185 26 85 41
185-205 12 97 15
205-225 2 99 3
225-245 1 100 1