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Calculation Techniques

Data Interpretation problems judge the person’s ability to analyze data quickly. Graphs, charts and tables are given and a person has to find out the relevant data which is required in a question and then do a calculation on it. Good observation coupled with speedier calculation helps in cracking DI problems.  In the case of difficult problems, it becomes imperative to read the problem along with the options.  The approach to DI problems lies in understanding:

 

1.  “What is given” – See the given data carefully to see the time period, the units and the trend. Each data tells a story. See whether it is a rising or declining trend.

 

2.  “What is asked” – Look at the questions and locate which is the relevant data that is required for the question.

 

3.  “What are the approximations and calculations required” – Sometimes an increase between two years may be asked, or the percentage growth, or a ratio. Look at the desired values and do quick calculations to get the answer. Choices are a big help in selecting answers.

 

The student must ignore superfluous information. Sometimes large tables are given and not all the data is useful to answer the questions. Sometimes there is a combination of tables and graphs.  One must correlate the graphs provided and understand the relationship between the graphs, before actually attempting the question. Intelligent guessing can reduce calculations and in turn saves time.

 

Example 1



Study the following table and answer the questions that follow:

 

Number of Items (in lakhs) produced by six companies over the years

Year ®

Company ¯

1997

1998

1999

2000

2001

P

Q

R

S

T

U

38.5

53.4

48.6

76.4

56.5

10.6

68.6

62.7

98.9

72.8

65.4

72.8

63.5

82.5

86.4

48.5

96.5

78.6

91.5

92.8

52.6

99.8

82.2

102.8

89.5

78.4

103.4

88.9

110.7

98.4

 

 

 

Example

What was the percentage of numbers produced by Company P in 2000 to that produced by Company U in 2001?

 

Solution


Solution: First see what figures we need. Look at row P and continue till you hit column 2000. The figure is 76.4
Then look at row U and look under the column 2001.

The rest of the data is not required for this question.

So the fraction required to find percentage is (76.4/98.4) × 100.
If we do the calculation, we find it is not very easy.

Using approximation, we first round off the figures to 77/100. (Increasing the numerator and denominator by just a little bit to get round figures)

We now visually see that the answer is close to 77%.
So in this way we have avoided a calculation.
 

 

 
 

Important: While approximation, either increase both quantities or decrease both quantities, otherwise the error will be high.

 


 

Example 2

 

Example
 

What is the percentage increase in production for Company P from 1997 to 2001?
 

Solution


To find percentage increase, we need the figures of P in 1997 and in 2001.
We see that the percentage increase required is from 38.5 to 56.5.
 
The formula for percentage increase is: [New value – Old value]/[Old value] ´ 100
The figure required in this case is: [56.5 – 38.5]/[38.5] ´ 100 = 18/38.5 × 100.
 
We again see that it is a somewhat lengthy calculation. So we try approximation.
 
Rounding off by increasing both numerator and denominator, we can reduce the fraction to 20/40.
We then get the answer as 50%, but since we have increased the numerator more (compared to 18), we need to reduce the answer somewhat. So the answer would be around 47-48%. After getting this figure, the choices will tell us the choice that we need to tick. Note again that we have avoided a calculation.
 

 

 

Important:
 Do the increase/decrease judiciously. Also, take a look at the choices. If the choices are close, wide approximation cannot be done. However, if the answer choices are far apart, one can make good use of this technique.

 

 

Example 3

 

Examples


What was the share of production of Company Q in total production in 2001?

 

Solution
 

Share of Company Q is given by (Q’s Production/Total Production) ´ 100 = (72.8/496.4) ´ 100.
Using approximation, we can make this fraction as 70/490 [by reducing both numerator and denominator].
We see that 70/490 = 1/7 = 14% approximately.
 

 

Example 4

 

Example
 

Which company has shown the maximum increase in production between 1997 to 2001?
 

Solution
 

No calculation is required in such sums. See the figures for each company. We see that the maximum increase happens for Company Q, which goes from 10.6 to 72.8, which is about 7 times, which is not matched by any other company.
 

 

 





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