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INLY BOOK WITH GRADED EXERCISES
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- The Accredited Guide vo

DATA

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AND

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SffiiiIeilsI\œMW
For CAT, MAT, XAT,

IIFT, SNAP,

BANK

(PO/Clerk),

SSC (CGL/CPO), UPSC (CSAT} &
Other State PSC Exams, etc.

sK

‹g

ˆ

ANANTA ASHISHA

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The Accredited Guide vo

Interpretation
Pome pane AND nn.

Bà

—....

——“

ATA

ñ
For CAT, (AAT, XAT, IIFT, SHAP, BANKK IP/LEI) SoC
(CGL/CPO), UPSC (CSAT} & Cinar State P&C Exams ete,

ANANTA ASHISHA

So

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PREFACE

Books play an important role in the preparation of any examination and one ¢
importance of books while preparing for any competitive exam. Rook for Data Interpretation &
Data Sufficiency can be the source to get the concepts related to various topics whieh =
score well in the examination.
Data Interpretation is the major part covered in Quantitative Aptitude Section of any exam.

DIDS basically shows haw data is analysed to answer the questions that are asked, The

candidates preparing for specific examination prefer the books related to that particular exam

which includes each and every section but separate books for each section make students scors
better marks,
Importance of DI/DS is increasingly moving centre stage in today’s competitive examinations

The questions that are asked in different examinations are not easy to solve and one cannat solez

these problems without having a better practice, but once you know the basic concent behind it.
you can solve it in less time. The ACCREDITED GUIDE TO DATA Interpretation & DATA
Sufficiency will serve the students in the above discussed manner. This book has been pret
after 2 comprehensive research on the teachers who are involved in teaching of DI DS. The

value points incorporated in this book on the basis ofthe research make this back stand fara

part from other available books in the market.

Features of this book
Each chapter begins with a brief introduction that will make the students understand ditferent

concepts clearly and conipletely.
¥

Clear indication of the Types of Questions along with proper guidelines to solve them. Fach 1
question has separate Theory, Solved Examples and Exercise.

wv

The Exercise of each chapter has been graded as per difficulty and at the end, cumulzt
has been giver: which is divided into three parts ie, Base, Moderate and Advance leve!
fully solved.

Base level, Moderate Level and Advance level exercise covers all types of gu

Hons Le. aswed in

previous years’ examinations.
wv

Questions of different competitive examinations like CAT, MAT, CMAT, XAT,
MHT-CET, Bank (PO/Clerk), SSC (CGL/PO), Railways, UPSC (CSAT) & other state

questions etc, upto 2015 have been covered.

Ỉ

‘

However, I have put my best effarts in preparing this book, but if any error or
been skipped out, I will by heartly welcome your suggestions. Apart from all those, who fa

phí

in the completion of this book, a special note of thanks goes to Miss Jasika Khera and fc. fite
Chabbra without their support, the book could not have comie toits shape. Ravi Shank. and
Ravindar Rawat have given their expertise in the layout of the book. The cantribution ot Nr
Sachin Kumar and Ms Gaura Sharma for this book is also very special, warthy of great
ANANTS

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CONTENTS
1.

Analysis of Data

+ Data

Ơ

Data Tables

ô Data Interpretation

Ơ

BarGraphs

Ơ

Line Graphs

ô

:

Percentage

ôAverage
+

2.

3,

Y Mixed graph

Ơ . Case Studies

Types of Data Representation

Y

12-76

*

Parts of Data Table

+

Interpretation of Data of Table
Questions Based on Single Table

:

‘

«

Questions Based on Two or More Tables

+

Miscellaneous Examples

«

Cumulative Exercises

Bar Chart
+

77-131

PartsofaBar Chart

*

+ Interpreting the Bar Chart
+

General Pointsabout Bar Chart

*

Questions Based on Simple Bar Chart

+ Significance ofBar Chart

¥

Questions Based on More than One Bar Chart

¥

`

“Vertical BarChart
¥ Horizontal Bar Chart

4.

Miscellaneous Charts

Data Table

‘+

*“_

Grouped Bar Chart

CompositeBar Chart

+ Miscellaneous Examples
*

Cumulative Exercises

Deviation Bar Chart

Line Graph
++
+

3-11

v⁄_ Pie Charts

Ratio

+

:

PropertiesofLineGraph
PartsofaLineGraph

Representation of Dataas Line Grap
h
Single Dependent Variable Graph
More than One Dependent Variab
le

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132-180
+ Graphs with Two Scales
+ RangeGraph

+ Miscellaneous Examples
*

Cumulative Exercises

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Pie Chart or Circle Graph

5.

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181-332
Rasedon More thõn One P

Â
â

rts
PieChae
of anc
Import
LimitationsofPieCharts

«

Basedon Percentage Values

Miscellaneous Examples

*

Basedon Degree Values

Basedon Actual Values

Cumulative Exercises

*

Based on Exploded Pie Chart

233-285

Mixed Graph

+

+

Combination of Tableand Graph

Miscellaneous Examples

+

Combinationof Graphs

Cumulative Exercises

286-317

Case Studies
«Steps to Solve ‘Case Studies’

+

Cumulative Exercises

Miscellaneous Examples

318-340

Miscellaneous Charts

9.

+

Radar Chart/Graph

Scatter Diagram

«

Triangular Bar Diagram

Cumulative Excercises

+

Area Diagram

341-382

Data Sufficiency
+

Do's & Dont’s of Data Sufficiency

+ To find Necessary Statements
*

Chất

To find Unnecessary Statements

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Miscellaneous Examples
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— DATA INTERPRETATION
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Analysis of Data
Data
Data is a way lo represent instructions, facts or concepts in an organised format suitable for communication,

interpretation or processing, by humans of other aulomaticmodes. These data are represented in a number of organised
formats (like graphical format, tabular formal, pie charts etc), so that we can conclude any particular information from
them.

Data Interpretation
‘The process of deriving conclusion or inferences from the information given in an organised format of data is called
"Data interpretation’.

Duta

ˆ

interpretation forms one of the most critical areas of different general and entrance examinations. It counts 10-20

questions in the MBA entrance examination, 20-25 questions in Bank examination, 5-10 questions in SSC examination,

and its inherent concepts will help the students to
5-7 questions is CSAT examination etc, Therefore, its understanding

score maximum in different examinations.

‘The principles used in data interpretation are as below
1, Percentage

3. Ratio

2. Average

‘The abave principles play a vital role in solving the problems. Hence, we should have proper knowledge of the above
stated principles, Let us study these in detail,

1. Percentage

‘The term percent means for every hundred, A fraction whose denominator is 100, is called a percentage and the
numerator of the fraction is called the rate per cent. It is denoted by the symbol %.
t

eho

100

exe
100

Percentage is a very useful {ool for comparison in the analysis of data. For example, in their captaincy Sourav
Ganguly has won 127 matches out of 205 matches and Rahul Dravid has won 64 matches out of 140 matches.
This can however, be beller comprehended in a percentage form, which is for

.

127

success rile of Ganguly = m 100% =6195%

5

aye 4
success rate of Dravid =to 100% = 45.71%
This reveals that asa captain, Ganguly is more succcszf than Dravid.

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& Data Sufficiency
The Aceredited Guide to Data Interpretation

4
Percentage equivalent of imporarn kaos

entage
Interpretation of Data Involving the Perc
woh per cent xis mere oc ess than
sate 1,
Required pesee:

-

Va se cf x— Valse

ofY reo
Value ofy

_ Natseofy- Value oft og

x

Ole
.
a
wie

"
m%
topes
w

|

2
10

comparison is made,

Réle2.

1=102%

Sol.

woe
Íc.
fe

Ue.
Sol.

negative growth.

Find 79% of 429,

9% = BIR

5
5

1%

Ex4.

C2735

1%
.29
19% OF 429 = 3442 = 4.29=339

Find 361% of 2345.

361%
= (200+ 50+ 10+ 1)%

Japan

tay
Sof.

?
10% =-L x2346
= 234,5

m= x mse 2345

1800

1180

A8

760
s0
1860
1580

1218

increment in production of cars in 2008 over 2007

in India= 2—™
» so95, = 8.57%
in USA = 29-9

5 1008 = 4.419

900
in China = 186071760 590, = 5,68%
3760
in Jopan
= 15801500 995; = 535%
1500
in Maly= 2218760 y toge,= 55

100

23619 = 70354 11725 + 234.5 + 2345 28465
Very handy method is, 2345 251 ~ gạas
100

(It is just to make you understand the concept.
Jt Js also suggested that use less time consuming method.)

1160

How much per cent of 1795645 is 64598?

Clearly, only in one country ‘USA’ production of cars has increased

64598 % 100% =36%

1793645

But you are required to find the exact value as you have to

choose ‘only one option and only approximate value is

by less than $% in 2008 over last year.

Ex.

sufficient to solve your problem,

Therefore, approximate percentage =

178
180

ye = 333%

Find inhow many years the production of sugar hasdecreased

by more than 30% over the previous year?
Yeats
Pioduction

x 10%

=x 100%

(in million tonne)

Sol,

2004 | 2005 | 2006

2007 | 2008.

974 | 726 | S24 | 370 |

Methodl
Decrement in the production of sugar over previaus year

in 2005 =. 974-726 X 100% = 25.5%
974

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ng |

700

10

Required percentage =

Figuté (n 000 tonne}

Inia
T00
USA
900
China | 1760

50m = 4.x 23655 1172.5

Sof

Find in how many countries the production of cars has
increased by less than 5% in 200S over last year?
tay

⁄⁄472z4xE58z12

300% =3% 2345=7035

Ex 3,

Fofndthe rementage change is any value. sw compara to

If¢ is positive, then there is percentage increase in the value
ofx over y (or percentage growth) and if¢ is negative, then
there is percentage decrease (or percentage decline) or

Calculation of Percentage
(1.

(whens ¢y)

The denominator part contains the value with which the

4
đ
W

5
Zz

Value ef y

k
W

la

AT
x

4
ft
a
Mie wr
x
x

wre ote

"
x
Đ

5

(when x> y)

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Analysis of Data

5

in 2006 = 726 = 324 100% = 27.8%
726
324~
276
in 2007 =
100% = 47.3%
324
in 2008 = 276 — 184 100% S333
216

& Direction
Number

In this case, (- =
974

Step2.

074

—_

A
c
BD
E

“184

524

276

072

052

066

“Therefore, in two years (2007 and 2008), the production of sugar

has decreased by more than 40% over the production in the

previous year.
Rule3. No comparison can be made based on percentage value if
base value is not known. e.g. If the profit of company A
increased by 20% and that of company B by 22% compared
to previous year profit, then which company’s profit is
more this year? We cannot say because we do nothave the

Average is a single value that summarizes or represents the
general significance of a set of values.
Sum of all items in the group
Average=
=
=
Number of items in the group

A batsman’s performance can be expressed as the average

number of runs scored per innings rather than giving the scores

of individual innings.

eg. Let us say Virat Kohli scored the following runs in five

different innings inan ODI series 55, 45, 75, 35 and 95. Then, his
average score per innings in that particular ODI series
=

+

45+ 7+ 35+ 93 _ gy
5

Average isalso called the ‘mean’ or mean value of all the values.
TF x;, Xp, X5.--+%, be nnumbers, then their average ˆ

xịt tr
fn

Ext.

tấy

Find the average number of books sold over the period
2010-13,

2010 | 2011 | 2012 | 2013
Number of books | 1100 | 1250 | 1390 | 1500
Years

(b) 1310
{a) 1210
(e) None of these

(c) 1410

{d} 1411

Sol, (b) Average number of books sold over the period 2010-13
_ Total number of books sold over theperiod
Total number of years

1100+ 1250-4 13904 1500 _ $240 _ 1555
4

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4

five different disciplines

2

Ast | Commerce | Science | Management | Computer
Science

350 |

20

l4
| sso]
|280]

280

450

140

300

300
480
380

360
420

30

160
120
200

380
340
330

320

400

180

320

Ex.2. What is the average number of students studying
Commerce from all the institutes together?

(a) 356

(b) 360

{e) None of these

us

(@ 340

Sol, (e) Average number of students studying Commerce from all

institutes

previous year value.

2. Average

studying

Oisciptines

8

726

of students

from five institutes.

‘Thus, in two years 2007 and 2008, decreased in the production of
Sugar is more than 30%.
Meihod IT

Steps. 26 3 Be

(Example 2) Read the infarmation

carefully and answer ihe question that follows.

Total number of students studying
.
Commerce from all institutes
Total number of institutes

+ Reqnired average number of students
2604 320+ 300+ 4804 360_ 1720 vu

Following types make it easy to operate data while using average.
4G) Based on Average Per cent Change
In these types of questions, we have to find out the difference
between the current per cent average and previous per cent
average. It is called the average per cent change. If average
percentage of a variable is given in the question, then we use
the average per cent change in value of variable during a given

period of time.

~. Average per cent change during the period
_ Percentage change during the given period
Number of years (or months)

. Find the average annual percentage increase in number of
eycles over the period 2010-14?
2010 | 2011 | 2012 | 2013 | 2014
Years
55
47
|. 3B

25
Number oÍcyeles | 20
(355
(b) 3253
(@) 4553
(©) None of these
Sol. (c} Number of cycles in 2010= 20
Number of cycles in 2014 = 55

(d) 42%

Percentage increase (ar change} in number of cycles daring
2010- = 222 x 1009 21755
Average percentage increase (or change) during 2010-14

__ Percentage increase during 2010-14 _ 1755. © gage,

Number of years during 2010-144

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& Data Sufficiency

The Accredited Guide to Data Interpretation

6
& Direction (Example 4)

n carefully
Y Direction (Example 5) Read the informatio
.

Read the information

and answer the question that follows.

carefully and answer the question that follows,

a company
Production figures of five types of scooter by
Total
:
Type of scooters
Years

Number of workers employed in

six units of a factory during the years
Years

writs |

8

`

e

5

E

F

120

140

136

112°

182

132

:

2009

145

88

118

2010

128

76

122

2011

136

96

132

124

158

140

2012

183

92

126

145

166

126

2014

152

110

146

128

175

150

.

L

2010
2011

2012

2013
"oor

z3 | 160 | tor | tạo | d6 | 170 | 146

Ex5.

Ex4. Find the average percentage increase in the number of
employed workers for unit D during 2011-12?
(a) 6.24%
(c) 8.87%

i

j

workers for unit D during 2011-12

=

20
“42

7
66

16
14

15
16

9
11

76
79

15

14

17

84

In which of the given years the production of type Ở
scooter was close to the average production of all the
.
:
scooters in the years?

{a) 2010

(b) 2011

*

(a) 2013

Production of O type scooter =8

=M.6=15

+. Difference with average =15—8 =7

Production of O type scooter = 12

5

In year 2012, average production = Me 17

In these types of questions, if the value of any variable is asked
and it comes close to any given option, then it is called the
closest value of the variable. For finding the closest value, we

should follow some steps which are as follow

Step 2. Find the difference = Any value (or entry)

-

— Averagc value

Minimum the difference, closer the value to the average.
Step 3. If the difference is same for any two different values

(or entries), then find the percentage deviation over the

Difference
`
average Le,
Average

Since, difference is same, so more the average, lesser the

percentage deviation, closer the value to the average,

Production of O type scooter.= 14

5

In year 2013, average production = “© = 15.2
Production of O type scooter = 15

5

¢-Caleu
% variation,
late because difference with average is same
(0.2) as15.2-15= 0.2

Step 1, Find the average value of the given period.

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8
12

In year 2011, average production = Sew

‘

(ii) Based on Closest Value

`

10
16

o

= 7 and it is very wide, so calculation not required.

x 1005 887%

124

26
2

14

N

15
18

ũ

73
Sol. (e} In year 2010, average production = —~

Number of employed workers for unit Din the year 2012= 135
Percentage change (or increase) in the number of employed
21357124 y toa
124

2

M

10
12

(c) 2014

Sof. (c) Number ofemployed workers for unitD in the year 2011 = 124

,

20
12

{c) 2012

(b) 7.14%
(d) 9.26%

{e) 5.24%

:

Zone

In year 2014, average production
Production of 0 type scooter = 16

T9

5

= 158

«Calculate % variation, because difference with averageissame

(0.2) as 16- 168 =0.2
Differe
"
TC
Now, % variation =.—
100)
Average ©
°
Since, the difference is same in 2013 and 2014, the year with more

average will have less % variation and will be closer to average
value. Average value of 2014 > average value in 2013. Hence, in

2014, the value (or production) of O type scooter is closer to the

average value of all the scooters in that year.

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7

Analysis of Data
Interpretation of Data Involving the Average

(iii) Average by Mental Calculation

follow some rules,

When the calculation of average would take a long time, itis

Rule 1. If the value of each item is increased by the same value k,

alternative, However, the actual calculation of average may
beneeded if more than one choicesare closer to each other,

While interpretating the data by average, we

which are as given below

then the average of the group of items will also be increase
byk.

For example,

Let the average marks of 50 students be 80, If we

increase the marks of each student by 1, then the
average marks of 50 students will also be increased
by 1.
ke

Rule 2.

8041=81

If the value of each item is decreased by the same value k,

then the average of the group
decreased by k.

of items will also be

better to do mental calculation and choose the (closest) best

& Direction

Production and exports of sugar (in million kg)
Years

ie.

Exports

207

189

209

215

220

421

561

587

645

680

Ex6.

mental calculation may work. Just observe that the exports

are, generily of ‘production withone year (2009-10) showing.

nearly ; of production as exports.
Hence, the required average will be> 2023. 'Thus,0.36looks

multiplied by k.

the closest among the alternatives given.

For example,

Let the average of 10 numbers be 90. IF we multiply
each number by 10, then the average of the 10

numbers will also get multiplied by 10.

`

.

If the value of each item is divided by the same value k

(where, k # 0), then the average of the group of items will

also be divided by k.

.

For example,

Let the average of 10 numbers be 90. if we divide
each number by 9, then the average of the 10.

numbers will also get divided by 9, i. oe 10.

Rule 5.

‘The average of a group of items will always lie between

smallest value and largest value .in the group, ie. the
average will be greater than the smallest value and lesser
than the largest value in the group.
For example,
Let 7, 10, 12, 11 be the set of four numbers, then

\|

A

Average

=

7410412411
:

40
=—=10
4.
which is greater than the smallest value of the set,
ie. 7and lesser than the largest value of the set, Le.
12.

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(d) 0.22

Sol. (©) None of the given options/chotces are closer toeach other, 50

then the average of the group of items will also be

Rule 4.

of the sugar production in the half decade was
{a) 0.49
(b) 0.41

(e) 0.11

80-1=79

90%10= 900

The average production of sugar exported as a fraction
(c} 0.36

Rule’. If the value of each item is multiplied by the same value k,

ie,

2008-10 | 2010-44 | 2011-12 | 2012-13 | 2013-14

Production

For example,

Let the average marks of 50 students is 80. If we
decrease the marks of each student by 1, then the
average marks of 50 students will also be
decreased by 1.

(Example 6) Read the information

carefully and answer the question that follows.

Weighted Average

When two groups of items are combined together, then we can

talk of the average of the entire group. However, if we know only
the average of the two groups individually, we cannot find out
the average of the combined group by items.

For example, there are two sections A and B of a class where the
average height of section A is 150 em and that of section B is
160 cm, On the basis of this information, we cannot find the

average of the entire class (of the two sections together). As
discussed earlier, the average height of the entire class

__sum of the total height of the entire class
total number of students in the entire class
In other words, if, is the average ofn, number, x, is the average
of 7, numbers, x, is the average of n, numbers and so on, then
MyXy + Ba; t+ MyXs +...

average of all(n, +, +...) numbers =
n+nạ+n, +...

. Ex7.

Ina class, there are 55 students and the following table
shows the number of students and their corresponding
weights.
.
Numberofstudents | 7 { 3 | 15413 | 6 | 9 | 2

‘Weights finkg). | 62 | 63 | 67 | 70 | 86 | zs | 95

Find the average weight of all the 55 students.
(đ)706kg
(Q714kg
(b)H6kg
()7z6*kg
* (e) None of these


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& D. ata Sufficiency
The Accredited Guide to Data Interpretation

8

(ii) Comparison of a Part of Its Whole
whole with the
Let us understand how to compare a part of its

Sol. (d) Required average weight

= 727X624 3XGS+ 15% OT + 13X70+ ó x80+ 9475+ 23 95

55
= 434+ 189+ 10054 910+ 480-4 675+ 190
35
= 3885
55
=?06 kg

help of following example.

over the years
Expenditure of a company (in lakh) por annum
soe
ma Years am
mm
Items of expenditure

3. Ratio
Ratio is compared by division of the measure of two

quantities of the-same kind. In other words, ratio is a
comparison of two numbers by division. If the two quantities
are x and y, then ratio of x and y is represented as xorx ty

y

The quantities
x and y are called terms of the ratiox: y,xisthe
first term or numerator
denominator.

and

y is the

second

term

or

e.g. if one has 3 oranges and 5 lemons in a bowl of fruit, the
ratio of oranges to lemons would be 3:5, while the ratio of
lemons to oranges would be 5 : 3.

‘There are mainly three types of ratio which aie as following
(i) Comparison of a Part to Another Part
Let us understand how to compare a part to another part with
the help of following example.

&f Direction (Example 8) Study the following table
carefully to answer the question that follows.
Years | Production of cars .

Countries

*

to the

total

respectively, is

on

expenditure

taxes

for all

the

years

(b}17: 11
(d) 13 : 102

(8) 11: 117
()12:101

Sol. (b) Expenditure on taxes in the year 2010=4.24 lakh and total
expenditure on taxes for all the years

53.16 44,244 936 + 10.42 = 27.78 lakh
2778

111

(iii) Comparison of One Whole to Another Whole
Let us understand how to compare of one whole to another
whole with the help of following examples.

& Direction (Example 10) Study the following
carefully to answer the question that follotus,

India

700

760

USA

900

940

2010

145 |

77 | 115 | 110

1760

1860

2011

Japan

1500

1580

128 |

82 | 122 | 115

2012

136.)

8B |

Italy

1160

1218

132 | 125

2013

186 |

92 |

125 | 135

.

Yeon

A

8

Sof. (c) Number of production of cars by India in 2013 =700

and number of production of cars by Japan in 2014 = 1580

+ Required ratio = 200

1580

23 95:79
79

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D

(b) 97: 119

(C) 113
: 92

(79:80

c

Ex 10. What is the respective ratio or total number of worker
s
employed in unit A for all years to the total number
of
workers employed in unit D for all the years?

(a) 119
: 97

(0) 35:79

table

Number of workers employed in four units of a
factory during the years

2014

What is the ratio between the production of cars by India
in 2013 to the production of cars by Japan in 2014?

(a) 35:77

10.42

Ex9. The ratio between the expenditure on taxes in the year 2010

2013

China

(b) 77:37

142
18.42

118
20
9.36

112
2
4.24

08
23.4
3.76

Fuel and transport
Interest on loans
Taxes

336

342

342

~~ 368

‘Salary

`
2 Regnired raio7 =-*ÊK
= TPMÀ (anprox)

Types of Ratio

Ex8.

table

&f Direction (Example 9) Study the following
carefully to answer the question that follows,

(d) 111: 97

Sol. (a) ‘Number of workers emplayed in unit A for
all the years

= 1454 128 + 136 + 186 = 505

`

Total number of workers employed in unil
D for all the years
11041154 1254-135 = 485

© Required ratio = 295.
485

"9
97

119. 97

t


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Analysis of Data

9

Ratio of Equality, Greater Inequality or

Lesser Inequality

Arratio is said to be a ratio of equality, greater or lesser inequality if
first term also known as antecedent is equal to or greater than or less
than the second term also known as consequent. In other words,

Rule3, Tofind the highest and the lowest among the ratio( <1),

when numerator < denominator.
Step1, Approximate the given ratio (if the number of digits in
numerator/denominator is more than 2).

+ The ratioa:b, where a= bis called a ratio of equality,

Step2. Multiply the numerator by 10 and get the resultant
fraction.

* The ratio a:6, where a> b is called a ratio of greater inequality,

Step3. Find only integer value of the resultant fraction.

:

eg. 323,535, etc,

e.g.5:3,7:5, ete,

* The ratioa:b

where, a < bis cailed a ratio of lesser inequality.
e.g. 224,628, ete,

° A ratio of equality is unaltered, a ratio of greater inequality is

diminished and a ratio of lesser inequality is increased, if the same

positive quantity is added to both its terms,
* A ratio of equality is unaltered, a ratio of greater inequality is

increased and a ratio of lesser inequality is diminished, if the same

positive quantity is not greater, then the smaller term be subtracted
.
from each of its terms.

» Students are advised that they should try assuming certain values
and check the results,
Interpretation of Data Involving the Ratio
Interpretation of data involving the ratio follows the following rules
Rule 1: To evaluate a ratio, 5/381 (say), where
numerator< denoininator, it is always better to reverse it
and divide 381 by 5 (reverse operation) as 381+5=76

Remainder 1, so the given rati ==
To find the highest-and the lowest among the ratio (< 1),
when numerator < denominator,
Step1. Apply reverse operation, i.e. straight away divide the
denominator of the ratio by the numerator to find how
many times the denominator is of the numerator.
Step2. Try to do mental calculation for comparing the ratios as
discussed below.
As the comparison of the ratios have been asked for, so

calculating the value of ratio will unnecessarily consume
some time,

1, Find the highest and the lowest amongst the following.
34

29

41

340" 602" 571° 741

Sol. Step 1. Apply reverse operation,
340

602

S71

741

14°34" 29° 41

Step 2. Number of times

-

maximum ratio will have the maximum value,

2. Find the highert and the lowest ratio amongst the
following.
e.g. The ratios areS71 284
+

685

me

393

849

“Sol. Step 1. Approsimated as

57 28 75(_13
oe ea
3)
Step2. Multiply by
Step3.

an, 510,
280, 130
68 39 15

Find the integer value,

>8
Further calculation is not required because

one fraction > 8 and other < 8.

Hence, 21 is the highest ratio and 724 is the lowest ratio.
685

Rule2.

14

Step 4, If any of the integer value of the resultant fraction are
same, then find the next decimal place and so on.
Step 5. Compare the value of the resultant fraction, The

393

Rule 4, To find the value which constitutes the maximum part

(or portion) or minimum part of the total value,
Ifand bare the two values constituting the total value

(a+b),

then

maximum

and

—*2.. is maximum,

when

4-6

is

is minimum,

when

a-b

is

ate

a+b

minimum.

@ Direction (Example 11) Study the given information
and answer the question that follows.
The total investment= Credit mobilised

+ Fund utilised and the value are given for different years

Years
€redit nobilised (X crore)

2010 |
800 |

2011 | 2012 | 2013 | 2014
0
1430 | 1520 | 1605

Fund utilised (® crore)

S60

680 |

795 | 980 | 320

Ex 11. Find in which year the credit mobilised constitutes the

24

17

4

4

19

18

[take only integer values]

Maximum value Minimum value

+

4

Lowest ratio

Highestratio

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maximum or minimum part of the total investment?
(a) 2010, 2014

(b) 2014, 2010

(9) 2011, 2012
(3) 2013, 2014
(©) 2012, 2013 _


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10

Ex 13. What is the respective ratio of amount spent by family on!
medicine to the amount spent on groceries?

Sol, (a) Step}. Assume, a= credit mobilised, b= fund utilised
Step 2. Finda ~ 6 for dilferent years as
659 725625
840
240
a-b>

(a)1:2

Maxam

Minimum

Hence, in 2010, credit mobilised constitutes the minimum part of
the total investment and in 2014 the credit mobilised constitutes

@®)13:21

(3:5
{d)14:23
{e) None of Lhese
Sol. (d) Expenditure of a family on medicine =39.6°
Expenditure of a family on groceries =828°

the maximum part of the total investment.
Hence, option {a) is correct.

cs Required ratio = 226 212 or 11:23

& Direction (Example 12) Study the information given
beloie to answer the question.
Expenditures ofa company (in? lakh) per annum over
the given year

23

828

.

Study the graph carefull:

Ef Direction (Example 14)

to answer the following question.
250

172

98:

Bonus

300

dalerest on Loans

23.4

¡

252
325

83108

Taxes

'

101

1A3

„

142

384,

368

:

3.96

46

'

364

48.4

4

fb) 10:23

(€)15:18
(d) 5:8
(e) 2a

Sol. {b) Required ratio

Total expenditure on taxes for all years
Total expenditure on fuel and transport for all years
83+ 108 +74 +88
+ 98

°

Ex 12. The ratio between the total expenditure on taxes for all years

and the total expenditure on fuel and transport for all the
years respectively is approximately
(a) 4:7

the question that follows.

Study the pie chart to answer

Degreewise breakup of expenditure
of afamily ina month

2008

2009

2010
Years

2012

2013

3175+ 225+ 100+ 175+ 225+ 200+ 250
= 1350

Total production of ¥ for all the seven years together
= 200+ 225+ 200+ 150+ 250+ 225+ 200
= 1450

Hence, required ratio =

1350

1450

. or 27:29
29

Important Formulae
+ Profit =SellingPrice (SP) ~ Cost Price (CP)
SP-CP
}

+ Profit percentage ‹

+ SP=
*CP=

x 100 l%

CPx (100 Profit/ Loss%)
100
SPX 100

(1004 Profit / Loss%)

* Total profit = Revenue — Expenses
Total amount spent in a month = £ 45800

2011

Sol. (c) Total production of X for all the seven years together

13

& Direction (Example 13)

2007

Ex14. What is the ratio between the total production o
commodities Xand Y for all the seven years together?
(a) 20:27
()13:14
(c) 27:26
(d) 14313
(e) None of these
-

98+ 112+ 101 + 133-4142
_ 451 _ 1 of 10:13 {approx}
586

150

8

;

°3

Salary

Fuel and Transpon

Production

8

hems of expenditure

* Per capita income = Total national income
Population.

+ Loss = Demand —Supply


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Analysis of Data

11

Types of Data Representation
An effective representation of data enables top officials to draw upon the inferences/information with the least effort and tine.
Therefore, it is required to organise the data into meaningful represcutation, The effective representation of data can be broadly classifed
into following

categories

+ Data Tables Data table is simplest method used for summarising data and representing it ina meaningful way. Ina table, data is arranged

systematically in columns and rows.

+ Bar Graphs Bar graphs are one of the easiest and inost commonly used tools of representing data. A bar graph consists of a group of bars,
which are equidistant from one another. The values in the bar charts are read by the measurement of the height of the bars,

+ Line Graph or X-Y Charts

The line graph simplifies the data interpretation, as itis pictorial representation of data and is therefore very

useful for determining trends and rate of change.

* Pie Charts

Pie charts are the cireular representation of data, This circular diageam is divided inte different sectors or segments.

+ Mixed or Combination Graph

Mixed graphs are the combination of more than one of the above discussed graphs to describe a real tife

situation and data is to be interpretated taking help of the given graphs collectively.
+ Case Studies In the case studies forin of data representation, the data is given in the form of a paragraph. One has to understand the data
represented in the paragraph and convert the same into a suitable form so as to interpret it meaningfully,
+ Miscellaneous Charts In miscellaneous charts questions based on a blend of different topics like bar graph, pie chart, etc. are being asked.

Forthisa candidate need to have a thorough knowledge of the required topics and should possess the required stilts to solve the different types

of questions.

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ae

ata Table
Tables are ‘often used in reports, magazines and | hewspapers

to represent a set of numerical facts. They

enable the
readers to make comparison of facts and draw quick conclusions. It is one of the
easiest and most accurate way of
presenting the data. They require much closer reading than graphs or
charts.
Itis the most systematic way of representing quantitative data in a tabular
form to understand the giveninformation
and to demonstrate
the problem in a

certain field of study. In a table, data is arranged systematically
in columns and
rows. Generally, ‘the information in arranged in a table in alphabetical
order, chronological order, monthwise,
yearwise, etc.
.

A

Parts of Data Table

table generally has the following five integral parts

1 Tabletitle

The title of the table gives a general ideaof the type and often
the purpose of information presented.
TILE
Stub

Column Headings

Body

`

Footnotes

2, Stub This section of the table contains
row headings that tell us about the specific
kind of information given in
that row.
.
3.

Column headings

4.'Body

The column headings tell us about the specif
ic kind of information given in that colum
n,

This section of the table consists of ‘numerical
figures or data.

5. Footnotes

This section of the table consists an additional
piece of information of the table.

i

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Data Tabte

13

e.g. The table given hetow shows the percentage breakup of people of different age groups in 4 different urban cities viz, Delhi, Mumbai,
Bengaluru and Pane in the year 2014,
Tablo titlo

X

Pergontage breakup of people of diffcrant
Ago groups {ycars) In 2014

Upto 20
»

Stub—>

‹

20-30

Dethi

12

18

3 | Mumbai
5
Bịngaluru

8
9

7
at

Puno

8

1g

30-40

40-50 | Above 5047

25

28

20

7
20,

96
23

20
27

3

1

23

Column

headings

Body ˆ

x®oal number of people survoyod is 15000000,

Footnotes

.

Interpretation of Data of Tables
The interpretation of data of the tables is done on the basis of assessment of
numerical figures in the light of interrelated column captions and style of the table.
In fact, more attention is focused on the relative position of different items

(subentries) in a table and questions are answered mostly regarding it.
1,
2.
3,
4,
5.

Maximum and minimum values.
Average value,
Maximum and minimum ratios af any two parameters in column/row,
Maximuny/mininum rate of increase/decrease.
Items showing eccentric behaviour

How to Interpret a Data Table

Here, data is presented in the form of simple table as given below
Number of employces working in various departments

Depariments
Years
2008
2009
2010
2011

Production | Markcling | Corporate | Rescarch
146
60
130
900
140
G4
146
B40
148
70
160
1000
180 `
72
180
1010

:
The above table shows

+ The number of employces working in production department

(in 2008 = 900, in 2009 = 940, Ín 2010 © 1000 and in 2011 = 1010)

+ Number of employees working in marketing department

(in 2008 = 130, 2009 = 146, in 2010 = 460 and in 2011 » 150)

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tmportant Points
Read both the question and data set
carefully. Understand what you are
being asked to do, before you begin

figuring out the information.

* Cheek the data and type of information
required. Bo sure that you are looking

at the right part of columns and rows
in table. +

* Increase your computation speed
(mental calculation). It is essential that
you develop an ability to calculate 1%,
2%, 15%, 25% of random numbers. You

should be able to calculate average of
six three-digit numbers in less than

30 seconds,

« Look at the footnotes given as they
provide additional information for

particular data. This explains the

jargons and lists the formulae that

might be needed to solve the questions

asked.

* Check the units required. Be sure that
your answer is in thousand, millions or
whatever, it is that the question

specifies.


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eH

a

{

11

Types of Questions Asked in Various Examinations

‘There are multiple types of questions which are asked from the chapter ‘Data Table’, so it is quite difficult topredict exact ‘ype
of questions that are asked but on the basis of Observation, Analysis and Experience, here are some different lành
questions that are usually asked in the examination. Almost all the questions in this chapter can be categorised into the

{
ị

*
i
ì

+ following types.

:

.

iene

Type @

Based on Single Table

Questions based on single table are asked in examinations. In these questions, a table having data is given. Based on theinformation given

in the table the questions asked are to be answered.

.

Examples Based on Type 1
The following table shows the marks obtained by two — Sol.(4)_ Intests Land, the average marks are minimum and thusa
score
in
đi
jects.
of 74 marks will be best relatively, whereas since range of ‘marks
students in different
subjects,
in test TI is upto 75, Thus, his performance is best in test I |
Subjects | StudentA | Maximum | StudentB

shin

English

60

History
Sanskrit

50
30

Psychology

marks

100

70

| Maximum
marks

80

100

150

70

100
50

100

60
16

comparatively.

( Đựếcếtion

(đ)zero

= _( 604704 50430

soon (22 x00

100+ 100+ 100+ 50
350
Me
ti
Ít
ks
o
f
student
làn aetna toe ae marks of s 20 . B

= (SERS
.

|

com = (Ben
-

2009 is shown.
States

= 60%
\3

Difference in mean aggregate percentage mark = 60~60=0%

Clearly, the difference in mean aggregate percentage of marksis
zero.
2//Consider

the

,

following

information

regarding

the

perform
in four different
fests
, ance of a class of 1000 students
UPSC (CSAT)
2012

Marks/Tests |

Average

marks of
Range
Tks

i

lỊ

60

301090

-

ft

60

|

70

W

which one of the following tests his performance is
the best

(a) Test
(o
Test

VUES

I

%0)(a) Test
Test I1V

Dy_Cannocaniter

2006

2009

‘a7

46

7.3

Punjab
R

3.8

7.4

so

34

47 | 52 | 80 |

65

R
6m
isthe difference between the total production of rice
{in tonne) to all the three states {UP, AP
and Punjab)
together in 2006 and 2008, respectively?
(2) 54 tonne
®)4

is

th

) 4.8 tonne

td) 4.4 tonne
.

o.

at is the average production of rice (in tonne) of state
une fe all the years ar
L

mne

{C5 tonne

\¥

2008

56

4,/What

V2

2007

UP

(c)
tonne
{e) None of these

80

go 75 | 2010100 | oto 100

~

Years

5.1

—-

Ifa student scores 74 marksin each of the four tests,
then in

comparatively?

.
Production of rise (in tonne)

ÁP

= 60%

CGPSC 2013

In the following table, production of rice (in tonne) of three
different states UP, AP and Punjab over the years 2006 to

.

Sol.{gy’ Mean aggregate percentage marks of studentA

Study the table carefully

‘and answer the questions given below.

100
25

‘The difference in the mean aggregate percentage marks of
the students is
`
- UPSC (CSAT) 2014
()25%
7
(b) 13.75%
(©)
125%

.

(Examples 3-5)

A None of these

5.05 tonne

(d) 4.6 tonne

Whatisi thePercentage increase
z in the producti
on of rice in

the state AP in the year 2009 in comparis
on with 2007?
70%

Đ 40%

( 55%

có 25%

°

(e) None of the above


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`

:

rection (Examples 7-11) Study the following table

carefully to answer these questions.

. (df «. Total production of rice (in tonne) of all the three states
(UP,

ÁP and Punjab) together in year 2006 = 56+47+38 = 141
and total production of rice (in tonne) of all the three states (UP,

Numbel of students appeared and Passed in an examination

from five different schools over the years.

AP and Punjab) together in year 2008 = 4.6+8.04 59=18.5

Schools

+, Difference between total production of rice (in tonne) of all

op

{@

In year 2007, production of rice in state AP = 5. 2tonne

2010 | 600 | 380 | 450 | 250

In years 2009, production of rice in state AP = 6.5 tonne

2011
2012

2013
2014

SPs

s2

(2 x00)
%2

= 25%

Hours

(nkm\)

Totalpayment

8

20

2120

B

10

2

1950

¢

9

24

2064

D

1

22

1812

be the total distance and p be the total payment.
2. Total payment = (Rate per kilometer x d)

.

s(em of diesel per Iteex)

m

pxsarsr(2)aar(s+2)

2.§peed,s= SP...

+ (6m+400)

(6m+40)

.

(d) 295 ; 286

(a) 74%
(o) 76%

we

(b) 75%
(a) 72%

For school D, which year had the lowest number of
students passed with respect to those appeared?
{a} 2010

(b) 2011

về ()2012

(a) 2013

During 2012, which school had the highest percentage af
students passed with respect to those appeared?

`

@)B

A

;

_ So, the speed of Car A= 28 9
"

SOLUTION

(đ}E
(Examples 7-11)

7. (d) Average number of students passed from school B
= 250+ 300+ 2804+320+380 .139
5

5

Average number of students passed from school C
— 350+ 420+ 4004 450+ 480 = 2100

Car B=2
s

5

4

(b) 70: 53
(d) 51:70

fac

We know that the mileage, time taken and total payment ofeach
car and hence we can find out their speeds.

CarC=Ÿcơ

$80 | 350 | S80 | 460 | 620
580 | 420 | 600 | 480 | 650
500
560 420 | 580
580 450 620 450 | 660
580 480 | 640 | 520 | 680

schools together in 2013? (rounded off. to the nearest
integer)

total distance/total time taken.

which gives us total distance, d=_P™

300
280
320
380

.%* What was the overall percentage of students passed with
“respect to the number of students appeared from all the

48) Car D

m

|
|
|
|

(c) 286 : 277

Letsbethe average speed, tbe the time taken, mbe the mileage,d

mộ

480
420
480
500

a

<

vA What is the ratio between the total number of students
appeared from all the schools together in 2010 and 2011?

(a) 286 + 295
(b) 277 : 286

Which car maintained the maximum average speed?
(a) Car A
(b) Car B

Sol, (0) Average speed ofa caris equal

|
|
|
|

(a) 70:51
{53:70
ˆ

(n9

A

()Carc

280
300
400
450

§

<<

years?

DPSC (CSAT) 2015

Mileage

|
|
|
|

3

passed from schools B and C respectively for all the given

diesel at $40 per L. In this context, consider the details
Cars

580
640
650
680

QB

5

„Z⁄ What is the raio between average number of students

6. Four cars are hired at the rate of 6 per km plus the cost of
given in the following table.

|
|
|
|

D

)

Passed

4

~\ Required percentage increase -(

e

Appeared

4

Years

Passed

.

the three states (UP, AP and Punjab) together in years 2006 and
2008 = 18.5-14.1=44 tonne
4. - $B) Average production of rice of state Punjab
cản38+74+ 3944 2P sos tonne

Passed

(Examples 3-5)

883858

SOLUTION

15

Passed

DalaTable

/>
+

Car
D= #3 <9

53

Therefore, only car A has speed greater than 9 and it is the

fastest car.

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5

++ Required ratio = ae

= 51:70

5

8. (8) Required ratio = (600+ 4504 520 + 580+ 620)

= 277012860
277: 286

+ (580+ 480 + 550+ 600+ 650)