Data Interpretation

Unraveling the Purpose of Data Interpretation Data Interpretation section virtually puts a student in the shoes of a Business Manager,

who is inundated with useful (and not so infrequently with useless) data and has to make

some quick interpretation of the data to reach important decisions. Once presented with

graphs or tables, the mental processor of a manager starts whirring at the top gear and

selects, prunes, manipulates, and compares the data and reaches certain conclusions.

Successful operations of these processes require that a manager possesses qualities like:

o An eye for detail, o An ability to focus on key issues quickly, o An ability to work on numbers in different ways, o An ability to see a trend, o An ability to identify exceptional situations, o An ability to work with logical relationships and o An ability to reach a conclusion using deductive logic.

Let us see how some of these qualities are tested using a set of questions picked up from

CAT 2001.

Question 1 to 3

There are six companies, 1 through 6. All of these companies use six operations, A

through F. The following graph shows the distribution of efforts put in by each company

in these operations.

A, 17.7 A, 18.5 A, 16.4 A, 18.5 A, 15.1 A, 15.6

B, 17.6 B, 16.7 B, 16.4 B, 10.3 B, 16.1 B, 17.6

C, 9.3 C, 10.9

C, 8.2C, 13

D, 15.7D, 7.4

D, 16.3

D, 11.2

D, 7.7

D, 11.8

E, 23.5

E, 25.9

E, 21.8

E, 28.6E, 28.6

E, 23.6

F, 15.7F, 22.2 F, 18.2 F, 23.4 F, 19.7

F, 17.6

C, 13.8C, 9.8

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 2 3 4 5 6

Company

% D

istr

ibu

tio

n o

f E

ffo

rt

Q1. Suppose effort allocation is interchanged between operations B and C, then C and D,

and then D and E and if companies are then ranked in ascending order of effort in E, what

will be the rank of company 3?

1. 2 2. 3 3. 4 4. 5

Q2. A new technology is introduced in company 4 such that the total effort for operations

B through F gets evenly distributed among these. What is the change in the percentage of

effort in operation E?

1. Reduction of 12.3 2. Increase of 12.3

3. Reduction of 5.6 4. Increase of 5.6

Q3. Suppose the companies find that they can remove operations B, C and D and re-

distribute the effort released equally among the remaining operations. Then, which

operation will show the maximum effort across all companies and all operations?

1. Operation E in company 1 2. Operation E in company 4

3. Operation F in company 5 4. Operation E in company 5

Answer to Question 1

After the first interchange, efforts of operation C become equal to that of the operation B

and vice versa. In the subsequent interchange between C and D, the efforts of C, which in

the question were of B, were allocated to D. In the last inter-change, efforts of E became

equal to that of the D. Thus in effect, the efforts of operation E after 3 inter-changes are

equal to that of the operation B before the start of inter-changes. In effect, the question

requires ranking of Company 3 if efforts in operation B are arranged in an ascending

order. The answer to the question is 3. The question is thus testing logical reasoning. The

fact that a graphical representation has been used to test this skill is almost like a clever

decoy placed by the examiner. Successful CAT takers learn the knack of quickly

identifying the root of the problem, rather than getting caught up in unnecessary details.

Answer to Question 2

Since operation E has the highest allocation, redistribution of efforts equally among

operations B to F will reduce the allocation of operation E. Hence, answer choices 2 and

E as well as to operations B, C, D and F would be 23% each. This is not feasible. Hence

allocation to operation A is 18.5. Therefore, allocation to all other efforts is 81.5 (100

18.5). Dividing this equally among 5 operations allocates 16.3 to each activity. Hence the

reduction is 12.3 (28.6-16.3). The question therefore requires not just logical reasoning

but also the ability to work on numbers in different ways.

Answer to Question 3

This question can also be handled with equal ease. Compare operation E with operation F

in company 5. The effort allocation is higher for operation E than for F, and will remain

so after redistribution of efforts of operation B, C and D equally among the remaining

4. In both cases, operation E requires 28.6% effort. By visual inspection, we can see that

the combined efforts of operations B, C and D in company 5 are higher than that of in

company 4. It implies that allocation will be more in company 5 than in the company 4

and thus choice 2 is also eliminated. Between operation E of company 1 and operation E

of company 5, the latter has about 5% more allocation before redistribution. If the choice

1 is to be the correct answer, the cumulative allocation of B, C and D for company 1

should exceed that of company 5 by 15%. Since that is not so (once again by visual

comparison of allocations), the correct answer is operation E in company 5. Dear CAT

aspirant, which of the qualities listed above are thus tested here?

It must be evident to you now how certain qualities are tested in DI. The good news is

that these are innate qualities in most people but the bad news is that they do not know

how to use them. Quite unfortunately, the plethora of training and coaching institutes also

have not understood the real reason for the DI section and inundate students with non-

essential short-cuts and techniques.

mastery on data interpretation.

Speed Builder-1: Master Ratios Most questions on DI require computation of ratios, percentages, rate of change, average,

maximum, minimum, count or data sorting, of which, ratio is the most common and

challenging operation. Some techniques for their quick estimation are presented below.

really required is an ability to estimate approximate values quickly.

Technique-1 Effective if numerator > > denominator

Round off numerator to nearest 1, 10 or 100 depending upon the magnitude of its value,

find quotient and compare.

Example: Which ratio is greater 7

319

or

3

122?

7

319

7

320

and its quotient = 46

3

122

3

120

and its quotient = 40

Hence, the first ratio is bigger.

Technique-2 Effective if numerator < < denominator Inverse all fractions and use Technique-1. The fraction with lowest quotient is biggest

and the one with highest quotient smallest.

Technique-3 Effective if numerator < denominator Find the differences between the numerators of two fractions and similarly between the

denominators.

If the difference between numerators is greater than or equal to the difference between

denominators, then the fraction with higher value of numerator is bigger.

Example: Compare 19

12

with

29

23.

Here the difference between the numerators of both fractions is 11 and between the

denominators is 10. Hence 29

23

is the higher of the two numbers.

Similarly, between 47

29

and

65

47,

the latter is bigger because differences between

numerators and denominators are 18 each.

Technique-4 Significant difference between the numerator and denominator

values of two fractions

Multiply numerator and denominator of fraction with small values with an appropriate

number and then compare

Example: Compare 181

117

with

19

12.

Multiply numerator and denominator of the second fraction by 10. After multiplication,

atorsdenobetweenDifference

numeratorsbetweenDifference

min__

__ = 9

3, which is less than the first fraction, hence the

second fraction is smaller.

The above-mentioned techniques can also be applied to percentages because a percent is

a fraction multiplied with 100.

Speed Builder -2: Think Smart Some smart thinking can make solving DI problems very simple for the students taking

the CAT. In my teaching at Career Plan, this is what I stress upon the most. I feel it is

important to eliminate some myths about how to prepare oneself for this section. The best

way to illustrate this approach is through an example taken from CAT 2002.

Question 4 and 5

Answer the questions based on the pie charts given below:

Chart-1 shows the distribution by value of top 6 suppliers of MFA Textiles in 1995.

Chart-2 shows the distribution by quantity of top 6 suppliers of MFA textiles in 1995.

The total value is 5760 million Euros (the European currency). The total quantity is 1.055

million tonnes.

Q4. The country, which has the highest average price, is

1. USA 2. Switzerland 3. Turkey 4. India

Q5. The average price in Euro/ kg for Turkey is roughly

1. 6.20 2. 5.60 3. 4.20 4. 4.80

Answer to Question 4

Conventional approach to solving the problem is to compute the average prices of all 4

countries and compare the values.

USA = 105515.0

576017.0

x

x

Switzerland = 105511.0

576020.0

x

x

Turkey = 105515.0

576016.0

x

x

India = 105526.0

576020.0

x

x

You would note that all values contain a factor of1055

5760. This factor can be ignored

because you are required to identify the country having the highest average value, not the

average value itself. Hence, you have to just compare 15

17, 11

20,

15

16

and

26

20. Obviously,

Switzerland gets the highest average price. Smart thinkers can easily solve this problem

by observation without writing even a single number on paper.

Pakistan, 12%

China, 15%

Turkey, 16% USA, 17%

Switzerland, 20%

India, 20% Pakistan, 16%

China, 17%

Turkey, 15% USA, 15%

Switzerland, 11%

India, 26%

Answer to Question 5

This question can also be answered by some quick mental calculations. The overall

average price for all countries is about 5.5 (1055

5760

105

570).

For Turkey, share of value to

share of quantity is 15

16, which is slightly more than 1. Average price for Turkey should

be a multiplication of these two ratios. Hence, the answer will be roughly 5.60.

Clearly, the examiner is not testing how quick you are with a series of calculations, but

wants to find out those who use a combination of common sense and smart thinking to

quickly and efficiently arrive at the final answer. This is their way of finding future

managers and leaders, who will always need to take the right decisions under severe time

and resource constraints.

Question 6 to 7 (Source: CAT 2004)

The profitability of a company is defined as the ratio of its operating profit to its

operating income, typically expressed in percentage. The following two charts show the

operating income as well as the profitability of six companies in the financial years

(F.Y.s) 2001-02 and 2002-03.

Operating Income

0

50

100

150

200

250

300

350

A B C D E F

Company

Op

era

tin

g In

co

me

(C

ro

re

s)

FY 01-02 FY 02-03

Q6. Which company recorded the highest operating profit in F.Y. 2002-03?

1. A 2. C 3. E 4. F

Q7. The average operating profit in F.Y. 2002-03, of companies with profitability

exceeding 10% in F.Y. 2002-03, is approximately:

1. 17.5 crore 2. 25 crore 3. 27.5 crore 4. 32.5 crore

Answer to Question 6

Profit is operating income x profitability. Comparing company A with company F, both

income and profitability of F are higher, hence Choice (1) is eliminated. Compare

Profitability

-5%

0%

5%

10%

15%

20%

25%

A B C D E F

Company

FY 01-02 FY 02-03

company F with company E, income of E is slightly lower but its profitability is almost

twice. Choice (4) is therefore eliminated. Comparison between C and E requires a closer

call. Income of E is only marginally lower than C, but its profitability is distinctively

higher (Profitability of C 15% and of E 17%, hence % difference =

100*15

1517>

10%). Hence, company E has the highest income.

Answer to Question 7

Rs. 30 cr. The profit of E is higher than that of C. Hence average should be more than

Rs. 30cr. Therefore the correct answer is (4).

What are some of the key lessons from these examples? How can this learning be used to

build up your speed? Quite obviously, what is required is an ability to look at problems

from different angles and an ability to simplify a seemingly difficult question. If you can

develop these abilities, you performance will improve dramatically in DI. This ability is

es of

TWI are also available in the form of a book authored by Mr. K. Venkataraman, Founder

of the TWI Foundation and a Director at Career Plan. I would strongly recommend this

book to those students who have a mortal fear of numbers and a still want to do well in

exams like the CAT!

Speed Builder 3: Logical Reasoning CAT questions increasingly require logical reasoning rather than the ability to perform

some quick calculations and intense number crunching. Very often, the questions require

students to understand the implications of the conditions imposed, observe the

relationships between data, and use deductive logic. Two examples taken from recent

CATs are presented here for illustration.

Question 8 to 10 (Source: CAT 2003) The table below provides certain demographic details of 30 respondents who were part of

a survey. The demography characteristics are: gender, number of children, and age of

respondents. The first number is each cell is the number of respondents in that group. The

minimum and maximum age of respondents in each group is given in brackets. For

example, there are 5 female respondents with no children and among these five, the

youngest is 34 years old, while the oldest is 49.

Q8. The percentage of respondents aged less than 40 years is at least.

No of Children Male Female Total

0 1 (38, 38) 5 (34, 49) 6

1 1 (32, 32) 8 (35, 57) 9

2 8 (21, 65) 3 (37, 63) 11

3 2 (32, 33) 2 (27, 40) 4

Total 12 18 30

1. 10% 2. 16.67% 3. 20.0% 4. 30%

Q9. Given the information above, the percentage of respondents older than 35 can be at

most.

1. 30% 2. 73.33% 3. 76.67% 4. 90%

Q10. The percentage of respondents that fall into the 35 to 40 years age group (both

inclusive) is at least

1. 6.67% 2. 10% 3. 13.33% 4. 26.67%

Answer to Question 8

interpreted as:

If minimum and maximum age in a group 40, then no respondent meets the condition

Therefore, number of respondents meeting the above criteria is 9 as shown in the Table

below. Hence 30% is the correct answer.

Answer to Question 9

If minimum and maximum age 35 then, all respondents meet the condition

Therefore, correct answer is 76.67%.

Answer to Question 10

No. of

children

Male Female

Total = 9

0 1 1

1 1 1

2 1 1

3 2 1

No. of

children

Male Female

0 1 4

1 0 7

2 7 3

3 0 1 Total = 23

If both minimum and maximum ages are < 35 or > 40 then no respondent meets the condition

If both minimum and maximum ages are 35 to 40 then all respondents meet the condition

If minimum < 35 and maximum between 35 to 40 then at least 1 respondent meets the condition

If minimum is between 35 to 40 and maximum > 40 then at least 1 respondent meets the condition

Lets look at one more set of questions, this time from CAT 2004.

Question 11 to 12 (Source: CAT 2004) In a Decathlon, the events are 100m, 400m, 100m hurdles, 1500m, High jump, Pole-

vault, Long jump, Discus, Shot put and Javelin. The performance in the first four of these

events is consolidated into Score-1, the next three into Score-2, and the last three into

Score-3. Each such consolidation is obtained by giving appropriate positive weights to

individual events. The final score is simply the total of these three scores. The athletes

with the highest, second highest and the third highest final scores receive the gold, silver

and bronze medals, respectively. The table below gives the scores and performances of

nineteen top athletes in this event.

No. of

children

Male Female

0 1 0

1 0 1

2 0 1

3 0 1 Total = 4