UNIT-III: DATA INTERPRETATION

What is Data Interpretation?

Data Interpretation is the process of making sense out of a collection of data that has been
processed. This collection may be present in various forms like bar graphs, line charts and
tabular forms and other similar forms.

Tips To Solve Data Interpretation Problems:

• Never try to reach final answer as it is not asked. You need to find whether the
information provided is enough to solve the given problem or not.
• Never make any assumption. Use only universal rules { eg. a + b = a + b - (a U b) }
• Try to solve questions by using above strategies
• Solve question step by step. First try to find answer using first statement then second
and finally with both then mark the answer
• Even if you find answer with only one statement, then try to find answer with
remaining statement as sometimes there is an option that answer can be find with both
statements separately.
• Move on quickly and mark answer can’t be found in case you are unable to reach
any conclusion with information provided.

1.Problem figures;

Answer figures;

A. 3
B. 5
C. 1
D. 2
Correct Answer: A

Explanation:

The shaded portion moves one step ahead clockwise. Also, an extra portion gets shaded after one
step. So, the answer figure 3 will continue the series.

2. Observe the problem figures given and select one option from the answer figures which
will continue the same pattern followed in the problem figures.

Problem figures;

Answer figures;

A. 4
B. 5
C. 3
D. 1
Correct Answer: A
Explanation:
In each step, the last sign becomes the first sign in the clockwise direction, and a new sign
appears in front of it. So, the answer figure 4 will continue the series.

3.Problem figures;
Answer figures;

A. 2
B. 4
C. 5
D. 1

Correct Answer: C

Explanation:

In figure B, the symbols interchange positions horizontally and in figure C, the symbols
interchange positions vertically, then in figure D, symbols interchange positions both
horizontally and vertically and so on. So, the answer figure 5 will continue the series

4.Problem figures;

Answer figures;

A. 4
B. 3
C. 2
D. 1
Correct Answer: D
Explanation:

The dot moves one step forward clockwise, and the arrow moves one step backward
anticlockwise. So, the figure that follows the mentioned pattern in 1. Hence, option D is the
correct answer.

5.Problem figures;

Answer figures;

A. 2
B. 3
C. 4
D. 5
Correct Answer: A
Explanation:

The symbols are moving one step ahead clockwise.

6.Problem figures

Answer figures
A. 4
B. 1
C. 3
D. 2
Correct Answer: A

7. Find out which one of the 4 figures is the missing part in the main figure.

(1) (2) (3) (4)

A. 1
B. 2
C. 3
D. 4
Correct Answer: C
Explanation:

Figure 3 is symmetry to the adjacent boxes.

8.Find out which one of the 4 figures is the missing part in the main figure.

(1) (2) (3) (4)

A. 1
B. 2
C. 3
D. 4
Correct Answer: B
Explanation:

Figure 2 follows the pattern.

9.Choose the correct water - image of the main figure from the given four figures.

Main Figure:

Answer Figures:

A. 4
B. 3
C. 2
D. 1
Correct Answer: C
Explanation:

As per the rules of water image the reflection of an object into the water is its water image.
It appears by inverting an object vertically i.e., upside down. Hence, option 2 is the
reflection among all.

10) Choose the correct water - image of the main figure from the given four figures.

Main Figure

Answer Figures
A. 1
B. 2
C. 3
D. 4
Correct Answer: D
Explanation:

As per the rules of water image the reflection of an object into the water is its water image.
It appears by inverting an object vertically i.e., upside down. Hence, option D is the correct
answer.

11.Problem figures:

Answer

Figures:

A. 3
B. 2
C. 4
D. 1
Correct Answer: C
Explanation:

The pattern is, the 2nd box is the 90 degree Anti-Clock Wise rotation of the 1st box and on of
the two shaded triangles is non shaded.

Only 4 in the answer figure, follows the same pattern.

12.

A. 3
B. 2
C. 4
D. 1
Correct Answer: C
Explanation:

The pattern is,

Consider small arrow as hour hand and long arrow as minute hand.

The hour hand in the problem figures makes 45 and 90 degree anti-clock wise rotation as a
cycle.

The minute hand makes 135-degree clock-wise rotation from one box to the other.

Following the same pattern, the answer figure must be 4 in the answer figures. So, option C
is the correct answer.
Data Arrangement
What is Data Arrangement?
Data arrangement problems (e.g., Seating Arrangement) test a person’s ability to interpret
complex data and fill in the gaps with the hints provided.

Structure of Data Arrangements Questions

Each Arrangement question usually starts with a paragraph that discusses a specific circumstance
and defines a few terminology. This introduction will offer you a sense of what you should do in
response to that inquiry. This will be followed by a few short lines outlining the rules or limits
that will be applied to the specific terms and circumstances. The seating arrangement of a group
of people is an often discussed question.

During arrangement questions, there are three different types of clues. They are:

1. Direct hints: The relationship between two terms will be mentioned immediately in the
statements in this category.

2. Indirect clues: These are laws that, once all other direct clues have been recognised, can be
transformed to direct clues by reasoning.

3. Scenario hints: Once all of the direct and indirect clues have been included into the logical
framework, the rest of the problem can be reduced to two or three scenarios, each of which will
lead to the correct solution after further examination.

Data Arrangement Questions

To answer the questions below, carefully read the following information:

Nine people A, B, C, D, E, F, G, H, and I are sitting in a row facing North in a movie theatre. B
is located at the far end of the row. Both F and G are seated next to H. C is directly to the right of
D, and third to the right of E. A is to the left of F. F is located third from the left of B.

Q1. Who is the middle person in the row?

(1) R

(2) D

(3) F

(4) H
Sol: We need to line up 9 people in a row. We’ll start with the direct information. It is assumed
that B is at one of the row’s ends. As a result, B might be at either end of the row. So here are the
two scenarios.

B______________________

The third position to the left of B is specified in the last paragraph, hence the first arrangement
will be rejected because there is no place to the left of B. Fixing F’s position in the second
arrangement gives us

_ _ _ _ _ _ _ _ _ F__ _ B There’s more information on A’s position in relation to F this time. F is

directly across from A. As a result, if we put A in his place, the arrangement will be _ _ _ A F__
_ B.

Simply keep looking for information that will connect the remaining people to those who have
already been sorted. It is assumed that H is seated next to F and G. So H falls somewhere
between F and G. As a result, we have _ _ _ A F H G B.

C is now in third place to E’s right. So there’s only one way E might be at the opposite end of the
spectrum. E _ _ C A F H G B is the arrangement. C is now to D’s immediate right. E I D C A F
H G B is the final layout.

As a result, A is seated in the middle of the row and option 2 is the right choice.

Q2. Who is on the opposite end of the line?

1.A

2.E

3.G

4) C

sol: E I D C A F H G B is the final layout. As a result, E is at the far end of the row. As a
result, the best solution is option 2.

Q3. Which of the statements below is correct?

1. E is two rows behind A.

2. D is on the far side of the spectrum.

3. I live next door to G.

4. Between F and C, there is one individual.

E I D C A F H G B is the final layout. As a result, the statement “between F and C, there is one
individual” is valid. As a result, the solution is option 4.

Cost of
Cost of
Side Base flooring
Field Height Radius fencing
Shape (in (in (in Rs.
Name (in m) (in m) (in Rs.
m) m) per sq.
per m)
metre)

A Triangle 16 12 50 20

10 ×
B Rectangle 30 15
20

18
C Square 15 40

D Parallelogram 20 12 60 25

E Circle 10 45 22

Q1. What is the cost of flooring of A?

a) Rs.4000
b) Rs.4600
c) Rs.4800
d) Rs.5000
e) Rs.4400

Ans: Option C
A is a triangle
So, area of A = 1/2 × 16 × 12 = 96 m2
So, cost of flooring of A = 96 × 50 = Rs.4800

Q2.What is the difference between the cost of fencing of C and that of B?

a) Rs.180
b) Rs.120
c) Rs.240
d) Rs.360
e) Rs.480

Ans: Option A
Perimeter of B = 2 (10 + 20) = 60 m
So, cost of fencing of B = 60 × 15 = 900
Perimeter of C = 4 × 15 = 60 m
So, cost of fencing of C = 60 × 18 = Rs.1080
So, required difference = 1080 - 900 = Rs.180

Q3. What is the ratio of the cost of flooring to that of fencing of field D?
a) 4 : 1
b) 6 : 1
c) 8 : 1
d) 9 : 1
e) 5 : 1

Ans: Option D
Area of D = Base × Height
= 20 × 12 = 240m2
So, cost of flooring of D= 240 × 60 = Rs.14400
Perimeter of D = 2 (20 + 12) = 64 m
So, cost of fencing of D = 64 × 25 = Rs.1600
So, required ratio = 14400 : 1600 = 9 : 1

Q4. The cost of fencing of field E is approximately what percent of the cost of flooring of
field C?
a) 10.5%
b) 19.46%
c) 18.71%
d) 15.36%
e) 13.82%
Ans:Option D
Perimeter of E = 2πr = 2 × 22 / 7 × 10 = 440 / 7 m
Cost of fencing of E = 440 / 7 × 22 = Rs.1382.85
Area of C = (15)2= 225m2
So, cost of flooring of C = 225 × 40 = Rs.9000
So, required % = 1382.85 × 100 / 9000
= 15.36% of flooring cost of C.

Q5. The cost of fencing of field C is what percent of the cost of fencing of field D?
a) 87.54%
b) 67.5%
c) 72.13%
d) 54.36%
e) 46.5%

Ans:Option B
Fencing cost of C = Rs.1080
Fencing cost of D = Rs.1600
Required % = 1080 / 1600 × 100 = 67.5%

Q: Read the following table carefully and answer the questions given below it. Data related to
number of students who got admission and who left the given five colleges 1,2,3,4 and 5 during
the given years.

COLLEGE 1 COLLEGE 2 COLLEGE 3 COLLEGE 4 COLLEGE 5

YEARS ADM LEFT ADM LEFT ADM LEFT ADM LEFT ADM LEFT

2008 161 - 148 - 179 - 116 - 128 -

2009 148 58 172 60 161 90 208 60 191 50

2010 135 69 188 96 143 101 169 45 167 79

2011 112 88 173 59 165 58 142 56 185 82

2012 141 39 151 48 179 66 155 108 142 91

Ques 1. What is the average number of students who got admission in College 4 during all the
given years taken together?
(a) 156
(b) 164
(c) 166
(d) 162
(e) 158
Average = (116 + 208 + 169 + 142 + 155 ) / 5
= 158

Ques 2. If the respective ratio of number of boys and girls in College 2 at the end of 2010 was
5:6, what was the number of girls in College 2 at the end of 2010?
(a) 212
(b) 186
(c) 208
(d) 192
(e) 172
Total admitted student till 2010 = 148 + 172 + 188 = 508
Total number of students who left till 2010 = 60 + 96 = 156
Difference = 352
Number of girls = 6/11 * 352 = 192

Ques 3. In which of the given colleges the number of students were the highest at the end of
2009?
(a) 1
(b) 2
(c) 3
(d) 4
(e) 5
College 1 = 161 + 148 - 58 = 251
College 2 = 148 + 172 - 60 = 260
College 3 = 179 + 161 - 90 = 250
 College 4 = 116 + 208 - 60 = 264
College 5 = 128 + 191 - 50 = 269
Ques 4. What was the total number of students in College 1 at the end of 2011?
(a) 335
(b) 347
(c) 329
(d) 363
(e) 341
(116 + 148 + 135 + 112 ) - (58 + 69 + 88 ) = 341

Ques 5. Number of students in College 5 at the end of 2009 is what percent more than the
number of students is College 3 at the end of 2009 ?

1 1 4 3
a) 95 b) 115 c) 35 d) 75

(5) Students of College 5 at the end of 2009 = 128 + 191 - 50 = 269

Students of College 3 at the end of 2009 = 179 +161 - 90 = 250

Percentage = (269-250) / 250 * 100 = 38/5

Ques 6. What is the respective ratio between total number of students who joined College 3 in
2010 and 2011 together and total number of students who left College 5 in 2010, 2011 and 2012
together ?
(a) 22:17
(b) 11:9
(c) 13:9
(d) 11:7
(e) 22:19
Ratio = (143 + 165 ) : (79 + 82 + 91 )
11 : 9

Sample Question
The table below shows the number of the mobile phones that were sold by the showroom in the
years from 2006 to 2010. Answer the below questions based on the information given in the table.
 Years / Showroom A B C D E F

2006 183 123 277 167 178 237

2007 178 272 269 95 379 198

2008 133 161 226 176 239 277

2009 264 107 237 225 282 237

2010 278 272 213 284 293 196

Q. How many percentages of mobile phones were sold by the showroom E in 2008 less than the
showroom A in 2010?
A. 10 B. 12
C. 14 D. 16
The total number of mobile phones there were sold by E in 2008 = 239.
The total number of mobile phones there were sold by P in 2010 = 278.
So, the reduction in percentage will be ((278 – 239)/278) * 100 = 14.02 %
As the values in the question are rounded off to nearest integer the correct answer 14%. So the
correct option is B.
Q. What will be an average number of mobile phones sold by all the showrooms in the year 2007?
A. 215 B. 222
C. 208 D. 213
We know the formula for the average which is total mobiles sold in 2007/number of stores.
Here total number of mobile phones = (178 + 272 + 269 + 98 + 379 + 198) = 1294
Number of mobile showrooms are 6.
So, 1294/6 = 215.66.
So the correct answer is 215.
Bar Graph
A bar graph is nothing but a pictorial representation of data wherein every independent variable
attains only discrete value. They are used for representing various types of data.
Types
There are types of bar graphs used to represent the data. They are as follows.
1. Simple bar graph
2. Composite bar graph
3. Stacked bar chart
4. Bar charts to show deviation
Simple Bar Chart
As the name suggests simple bar chart is the simplest bar graph of all. It is used to describe one
continuous variable along with the one discrete value. The figure below shows the proper
representation of a simple bar chart.

Composite Bar Chart

To solve the limitation of simple bar chart composite bar chart is used. We use a composite bar
chart to show two or more than two continuous variables on the same graph. This is the figure
below that describes how a composite bar-chart looks like.
Stacked Bar Chart
Stacked bar charts are used to represent the break-up of the content for continuous variables. It is
very convenient to use it for comparing different sets of data. It can be used to represent factors such
as revenues, profits, losses over a period of couple years. The figure below describes the same.

Bar Charts to Show Deviation

Mostly bar charts are used to show the deviation. And that is why the bar charts that are used to
show the deviation are very common. Deviation charts can show the deficit as well as the surplus,
imports, and exports, etc. It is usually required to represent the positive as well as negative values of
the continuous variables.
As shown in the figure a baseline is created wherein the positive values are shown above the line
while the negative values are shown below the line. Answer the questions based on the given figure
below.

Q. Out of the given years, in how many did the export was more than 10% as compared to the
import?
A. 1 B. 2
C. 3 D. 4
Answer: In the year 2000, exports were 60 while the imports were 50. So 10% of 50 is 5. And thus
the total will be 55. Here 60 > 55. Similarly in 2001, 110 = 10% of 100.
In 2002, 120 < 130. For 2003, 120 > 10% of 100. For 2004, 150 < 10 % of 140.
In 2005, 190 < 10 % of 180. So there are years i.e. 2000 and 2003 where exports were 10 % greater
than the imports. So the correct answer is B.
Q. For all the years mentioned what is the average of the exports?
A. 110 B. 120
C. 125 D. 130
Answer: Here from the figure the average of the exports will be: (60 + 110 + 120 + 120 + 150 +
190)/ 6 = 125. So the correct answer is C.
Q. From the numbers given in the figure below, what will be the average annual growth for the
imports done from 2001 to 2005?
A. 11 B. 12.5
C. 13.5 D. 14.5
Answer: Imports done in 2001 = 110
Imports done in 2005 = 190
So, the annual growth = (190 – 110)/110 * 100 = 72.72%
Now, the average growth will be 72.72/ 5 = 14.5. So the correct answer is D.
Q. From 2000 to 2005 in which was the growth in imports as compared to the previous years was
the highest?
A. 2001 B. 2002
C. 2004 D. 2005
Answer: From the figure, we can determine that imports grew only in 2001, 2002, 2004, and 2005.
For 2001, (50 * 100) / 60 = 83.33
For 2002, (10 * 100) / 110 = 9.09
For 2004, (30 * 100) / 120 = 25
For 2005, (40 * 100) / 150 = 26.66
Thus the correct answer is A. This type of questions can be solved quickly if you compare the base
for every year. Here for 2001, the base value is 60 and thus chances are high the growth in 2002
must have been higher. You can look for this in the exams and start by solving 2002. This will save
a lot of your time.
Q. In how many years does the export as well as import increases as compared to the previous
years. And among them, in how many years was the percentage increase in export was greater than
the percentage increase in imports
A. 0 B. 1
C. 2 D. 4
Answer: Out of all the years given in the figure, the imports and exports as compared to the
previous are increased in every year except 2000 and 2003. Out of the four in which imports and
exports have increased, in no year does the percentage increase in export is greater than the
percentage increase in imports. Thus the correct answer is A.
Practice Questions
Q. In the following graph, the increase in the wheat over years is shown. Based on this answer the
questions below.
1. How much does the wheat grow in 1994 as compared to the previous year?
A. 12.2% B. 13.6%
C. 16.1% D. 17.8%
Ans: The correct answer is C.
Q. What was an increase in the average rate of growth of wheat from 1993 to 1995?
A. 13% B. 12%
C. 14% D. 16%
Ans: The correct answer is D.
Q. How much percentage of growth of wheat was less in 1994 as compared to 1993?
A. 13.9% B. 12.2%
C. 11.9% D. 14.6%
Ans: The correct answer is A.
Q. What was the average of the total wheat, grew from 1995 to 1997?
A. 22 tonnes B. 26 tonnes
C. 28 tonnes D. 25 tonnes
Ans: The correct answer is B.
Line Chart
The line chart is nothing but an upgraded version of a bar chart. It is formed by connecting the
uppermost point of the bars so that we have a line. By repeating this following process, with other
bars as well we will get a line chart. The calculations can be tough but the main aim of the examiner
is to check whether you can apply logic to eliminate options and evaluate the graph thereby getting
the answer.

On the basis of the figure below answer the following question. In the graph, the number of boys
and girls are given in five schools. Study this graph properly and answer the questions.

Q. What percentage will be the number of girls in school A out of the total number of girls in all the
schools?
A. 15 B. 17
C. 22 D. 24
To solve this question there are several different approaches. Let’s look into each approach one by
one.

First method
For the first method, we can calculate the number of girls simply by adding all the girls in the
schools and then taking the girls from school A as the numerator thereby calculating the total
percentage of girls. For example, in this question, the total number of girls is 17750 and the girls in
school A as a part of all the girls in all the schools will be (2750/17750) x 100 = 15.4%
The major roadblock in this method is that it requires a lot of calculation and there are chances that
you may calculate in exam properly which might lead to silly mistakes. And that is why we have
given a second approach to this question.

Second method
This method is based on the estimation. In this method, you have to suppose a baseline and then
from the given options, you have to assume which is the closest to the answer. Suppose, there are 5
schools and every school has an equal number of 10 girls so the average will 10 and the percentage
will 20%. Same will be the case for 100 girls with 5 schools. Here the percentage will be dependent
on the number of schools.

In the above question also assume a baseline at the centre of the figure. As there are five schools
given in the question the percentage will be 20% but the base-line is above the number of girls in A.
So we can say that the number of girls in school A will be less than 20%. Thus options 3 and 4 can
be negated. Now for the remaining options when we look at E and compare it with A, there is the
larger difference and so 17% cannot be answered as well. Thus the remaining option is 15 which is
the correct answer.

This method should only be done when the options are not very close. Thus the correct answer is
(1).

Q. Which class has the percentage of boys and girls as part of the total students in all the
schools?
A. A B. B
C. C D. D
From the figure you can see the highest of boys and girls in one school is in D. As the base for all
the schools remains a same i.e. total number of students all the schools will be same for every
school then we can say that in school the percentage of students is the highest. Thus the correct
option is (3).

Q. Which school has the lowest number of students?

A. A B. B
C. C D. D
In school C the number of students is the lowest. Thus the correct option is (3).
Practice Questions
In the given figure number of laptops prepared by two different companies is given from 2004 to
2009. Answer the questions based on the figure below.

Q. What will be the difference in the number of laptops made by the company X in the year 2004
and 2005?
A. 10000 B. 20000
C. 30000 D. 40000
The correct answer is B.
Q. The production of the laptop by the company Y was how much percentage of the production by
company X in the year 2007?
A. 120 B. 148
C. 152 D. 164
The correct answer is D.
Q. For all the given years in the figure, what is the total number of laptops made by both the
companies?
A. 144000 B. 145000
C. 145800 D. 146200
The correct answer is C.
Q. What was the maximum difference between the manufacturing of laptop by both the companies?
A. 40000 B. 41000
C. 45000 D. 51000
The correct answer is D.
Pie charts

In pie charts, the entire diagram looks like a pie and the components in it resembles the various
slices cut from the pie. The pie-chart is thus used to show the break-up of one continuous variable
into its components parts.

For, the example you can see the distribution of sales of the laptop industry between five
companies:

Company % in market share

HP 22
 Dell 33

Lenovo 13

Asus 15

Acer 17

The pie chart represented above shows a circle of 360 degrees which represents 100 % of the values
of the continuous variable. Thus, 3.6 degree of the pie chart represents 1 % of the total values of the
variables being represented. Pie-charts are more versatile than the bar graphs, tables or two variables
graphs. It also represents the clear and precise data that needs to display. Thus, also helps you
establish the relationship between different sectors.

Venn Diagrams
Which of the following diagrams indicates the best relation between Travelers, Train and Bus ?

Answer: Option C
Explanation:
Bus and Train are different from each other but some travelers travel by bus and some travel by
train.