DATA INTERPRETATION
LECTURE - 2

TWO-VARIABLE GRAPHS
Here the data will be represented in the form of a graph.
Generally it represents the change of one variable with respect
to the other.
Look at the following graph:
Car sales in India in different years (in 000’s)
200
150
100
50
0
2003 2004 2005 2006
Maruti Hyundai Others

From the given graph, we can calculate
1. The percentage change in the sales of any brand from one
year to another.
EXAMPLE:
200
What is the percentage
increase in Maruti sales 150
from 2004 to 2006? 100
(1) 50% 50
(2) 75% 0
2003 2004 2005 2006
(3) 100%
Maruti Hyundai Others
(4) 125%

From the given graph, we can calculate
2. Rate of growth of total car sales (all the brands) in a given
period.
EXAMPLE: 200
What is the approximate 150
percentage change in the
100
sales of all the given
brands together from 2003 50
to 2006? 0
2003 2004 2005 2006
(1) 100%
Maruti Hyundai Others
(2) 120%
(3) 160%
(4) 200%

From the given graph, we can calculate
3. The proportion of the sales of any brand with respect to the
sales of any other brand in the given year.
EXAMPLE:
200
In 2006, the sales of
150
Hyundai is approximately
what percentage less than 100
the sales of Maruti? 50
(1) 25% 0
2003 2004 2005 2006
(2) 42.9%
Maruti Hyundai Others
(3) 60%
(4) 75%

From the given graph, we can calculate
4. For a given brand, the year in which the sales increased by
maximum percentage over the previous year.
EXAMPLE:
In which year the sales of 200
Maruti increased by 150
maximum percentage over 100
the previous year?
50
(1) 2004 0
(2) 2005 2003 2004 2005 2006
(3) 2006 Maruti Hyundai Others
(4) All are same

From the given graph, we can calculate
5. In a given year the brand which has noted the maximum
growth rate in the sales over the previous year.
EXAMPLE:
For which brand, the growth 200
rate in the sales is maximum 150
from 2005 to 2006?
100
(1) Maruti
50
(2) Hyundai
0
(3) Others 2003 2004 2005 2006
(4) Both Maruti and Hyundai Maruti Hyundai Others

BAR-CHART
Bar-chart is also one of the ways to represent data.
The data given in the above graph can also be represented in
the form of a bar-chart as shown below.
200 175
150 125
100 100 100
90
100 80
60 60
50 50
50 30
0
2003 2004 2005 2006
Maruti Huyndai Others
Here also we can deduce all the parameters as we could do in
the case of a two-variable graph.

From the given graph, we can calculate
1. Percentage change in the sales of any brand from one year to
an other.
EXAMPLE:
200 175
What is the percentage
increase in the sales of 150 125
Maruti from 2004 to 2006? 100
100
80
100 100
90
60 60
(1) 50% 50
50
30
50
(2) 75%
0
(3) 100% 2003 2004 2005 2006
(4) 125% Maruti Huyndai Others

From the given graph, we can calculate
2. Rate of growth of total sales of the cars (all the brands) in a
given period.
EXAMPLE:
What is the approximate 200 175
percentage change in the 150 125
sales of all the given 100 100 100
90
100 80
brands together from 2003 50
60
50
60
to 2006? 50 30
(1) 100% 0
(2) 120% 2003 2004 2005 2006
(3) 160% Maruti Huyndai Others
(4) 200%

From the given graph, we can calculate
3. Proportion of the sales of any brand with respect to those of
any other brand in the given year.
EXAMPLE:
In 2006, the sales of 200 175
Hyundai is approximately 150 125
what percentage less than 100
80
100 100
90
100
the sales of Maruti? 50
60
50
60
50 30
(1) 25%
0
(2) 42.9% 2003 2004 2005 2006
(3) 60%
Maruti Huyndai Others
(4) 75%

From the given graph, we can calculate
4. For a given brand, the year in which the sales increased by a
maximum percentage over the previous year.
EXAMPLE:
In which year the sales of 200 175
Maruti increased by a 150 125
maximum percentage over 100 100 100
90
100 80
the previous year? 50
60
50
60
30
(1) 2004 50
(2) 2005 0
2003 2004 2005 2006
(3) 2006
Maruti Huyndai Others
(4) All are same

From the given graph, we can calculate
5. In a given year the brand which has noted the maximum
growth rate in the sales over the previous years.
EXAMPLE:
For which brand the growth 200 175
rate in the sales is maximum 150 125
from 2005 to 2006? 100
100
80
100 100
90
60 60
(1) Maruti 50
50
30
50
(2) Hyundai 0
(3) Others 2003 2004 2005 2006
(4) Both Maruti and Hyundai Maruti Huyndai Others

VENN DIAGRAMS
If the information comes under more than one category, we
represent such data in the form of a Venn diagram.
The following Venn diagram represents the number of people
who speak different languages.
Hindi (80) English (120)
32 10
25
12
Punjabi (125)

From the given diagram, we can find
1. The number of people who can speak only English.
2. The number of people who can speak only Punjabi.
EXAMPLES:
How many people speak only
English? Hindi (80) English (120)
32 10
(1) 22 (2) 73
25
(3) 47 (4) 120 12
How many people speak only
Punjabi? Punjabi (125)
(1) 37 (2) 50
(3) 75 (4) 125

From the given Venn diagram, we can find
3. The number of people who can speak both Punjabi and Hindi.
4. The number of people who can speak exactly two of the three
languages.
EXAMPLES:
How many people can speak English (120)
Hindi (80)
both Punjabi and Hindi?
32 10
(1) 9 (2) 12
25
(3) 13 (4) 38 12
How many people can speak
exactly two languages out of the Punjabi (125)
given three?
(1) 25 (2) 35
(3) 60 (4) 80

From the given Venn diagram, we can find
5. The number of people who can speak at least two languages.
6. The number of people who can speak exactly one or two
languages.
EXAMPLES:
How many people in the colony
speak at least two of the above
three languages? Hindi (80) English (120)
(1) 25 (2) 35 32 10
(3) 60 (4) 80 25
12
How many people in the colony
speak only one language?
Punjabi (125)
(1) 32 (2) 73
(3) 75 (4) 180