Data Interpretation questions typically have large amounts of data given in the form of tables, pie-charts, line graphs or some non-conventional data representation format. The questions are calculation heavy and typically test your approximation abilities. A very large number of these questions check your ability to compare or calculate fractions and percentages. If you sit down to actually calculate the answer, you would end up spending more time than required. Here are few ideas that you can use for approximation.

Funda 1 Calculating (Approximating) Fractions

When trying to calculate (approximate) a fraction p/q, add a value to the denominator and a corresponding value to the numerator before calculating (approximating).

Example,

What is the value of 1789/762 ?

First the denominator. We can either take it close to 750 or to 800. Lets see how it works in both cases. We know that the answer is between 2 and 3, so for adding values / subtracting values from the denominator or the numerator, I will consider a factor of 2.5.

Case 1: 762 is 12 above 750, so I will subtract 12 from the denominator. Keeping the factor of 2.5 in mind, I will subtract 25 from the numerator.

My new fraction is,

(1789 – 25) / (762 – 12) = 1763 / 750 = 1763 ? (4 / 3000 ) = 7.052 / 3 = 2.350666

Actual answer is 2.34776.

As you can see, with very little effort involved in approximation, we arrived really close to the actual answer.

Case 2: 762 is 38 below 800, so I will add 38 to the denominator. Keeping the factor of 2.5 in mind, I will add 95 to the numerator.

My new fraction is,

(1789 + 95) / (762 + 3 = 1884 / 800 = 2.355

As you can see, even this is close to the actual answer. The previous one was closer because the magnitude of approximation done in the previous case was lesser.

Funda 2 Comparing Fractions

If you add the same number to the numerator and denominator of a proper fraction, the value of the proper fraction increases.

If you add the same number to the numerator and denominator of an improper fraction, the value of the improper fraction decreases.

Note: You can remember this by keeping in mind that,

1/2

and

3/2 > 4/3 > 5/4 > 6/5 …

Example,

Arrange the following in increasing order: 117/229, 128/239, 223/449.

Lets first compare 117/229 & 128/239.

If we added 11 to the numerator and the denominator of the first proper fraction, the resulting proper fraction would be 128/240, which will be bigger in value than the original (as per Funda 2).

We know that 128/240 is smaller than 128/239, as the latter has a lower base.

So, 117/229

? 117/229

Now lets compare 117/229 and 223/449.

If we added 11 to the numerator and the denominator of the second proper fraction, the resulting proper fraction would be 234/460, which will be bigger in value than the original.

If we doubled the numerator and denominator of the first proper fraction, the resulting proper fraction would be 234/458.

We know that 234/460 is smaller than 234/458, as the latter has a lower base.

So, 223/449

? 223/449

Using the above two results, we can say that 223/449

Note: This question can be solved much simply by just looking at the numbers and approximately comparing them with 12. I used this long explanation to illustrate the funda given above.

Following are a few other shortcuts that might come in handy during DI-related calculations.

Funda 3 Percentage Growth

If the percentage growth rate is r for a period of t years, the overall growth rate is approximately: rt + t * (t-1) * r2 / 2

Note: Derived from the Binomial theorem, this approximation technique works best when the value of ‘r’ is small. If the rate is above 10%, then this approximation technique yields bad results. Also, if the rate is 5% then r = 0.05; if the rate is 7.2% then r = 0.072.

Funda 4 Comparing Powers

Given two natural numbers a and b such that a > b > 1,

ab will always be less than ba

Tabular Form

Tabular form or Tables is an easy area to score marks in the aptitude section of IBPS, SBI PO and SSC exams. One or two problems in the exam are asked on Tabular form of Data Interpretation.

A tabular form is a representation of data in a table format. It is easy and convenient to represent data in a tabular form. The data is present in rows and columns and one can draw conclusions from it easily. It is the most organized method to represent data.

Let us now look at the different types of Data Interpretation questions that are asked from the tabular form.

Problem I: Total 24500 people who are in the given profession and (of these) percentage of female and males.

Question 1: What is the ratio of the total number of males in the medical and teaching profession together to the ratio of females in the same professions together?

*Tip: Ratio is the comparison of like terms in its simplest form.

Solution:

Step 1:

As we need to find the ratios, we use the formula
Males ( Medical + Teaching): Female ( Medical + Teaching)

Step 2: 
By substituting the values in the above formula
(40% x 11%x 24500)+(20% x 21% x 24500) : (60% x 11% x 24500)+(80% x 21% x 24500)

Step 3: 

By eliminating 24500 and percentage as it is common, according to the concept of ratio we get,
(40 x 11) + (20 x 21) : (60 x 11) + (80 x 21)

Step 4: 

By Simplification,
22 + 21 : 33 + 84
= 43 : 117 
Therefore, The ratio of total number of Males: Females in the medical and teaching profession together is 43:117
*Note: Don’t write the steps during examination as it consumes a lot of time. Directly jump to the step 3 as 24,500 is common and step 2 can directly be eliminated.

Question 2: Total number of people in the teaching profession is what percent of total number of people in law?

*Tip-In this question we are suppose to find the percentage change

Solution:
Step 1: 
As we need to find the percentage change, we need to use percentage formula
x is what of % of y  = (x/y)100 [Formula]
X-Total number of people in teaching program
Y- Total number of people in law

Step 2: 

By substitution,
(Total number of people in teaching program/ total number of people in law) x100

Step 3: 
By substituting values in the above formula,
(21% x 24500/24% of 24500) x 100

Step 4: 

By simplification,
21/24 x 100

Step 5: 

By simplification,
7/8 x 100
= 87.5%
Therefore, the total percentage of people in the teaching profession is 87.5% of the total percentage of total people in law.

Question 3: What is the total number of males from all the profession together? 

1) 11472  2)12784  3)12348  4)12453  5) None of these

Solution:

Step 1: 

As we need to find the total number of males in all the profession, we are suppose to take (the percentage of males in one profession x percentage of the total number of people in that profession x total number of people) and thus we need to add all the values together.

(40% of 11% of 24500)+(70% of 18%of 24500)+(55% of 24% of 24500)+(20% of 21% of 24500)+ (65% of 16% of 24500)+(56% of 10% of 24500)

Step 2: 

By Simplification,

(40 x 11) + (70 x 18) + (55 x 24) + (20 x 21) + (65 x 16) + (56 x 10)

= 5040

Therefore the answer is Option 5 – None of these.

In examination on average about 30 to 36 seconds are allotted to solve a question. Though this question appears to be simple the process of calculation is really lengthy as we cannot eliminate any number. The quickest way to solve this question is to skip the question or else leave the question for the end.

Question 4: The female in the Engineering professions are what percent of males in the management profession.

1) 71.71  2) 96.43 3) 83.16 4)68.54 5) None of these

Solution:

Step 1: 

As we need to find the percentage change, we use the percentage formula,

x is what percent of y = x/y x 100

x- Females of Engineering

y-Males of Management

Step 2: 

By using the percentage formula in finding out the female engineering profession percentage to male percentage in management profession

Females of Engineering/Males of Management x 100

Step 3: 

By substituting the values in the formulas,

30% of 18% of 24500/56 x 10 x 24500

Step 4:

By simplification,

30 x 18 /56 x 10 x 100

Step 5: 

By simplification

54/56 X 100

= 96.43%

Therefore, the answer is option 2 – 96.3%.

Remember don’t waste your time in writing down steps. Directly jump to step 4 and eliminate all unnecessary steps.Solve this sum on the bases of assumption, it will help you to save some time.