Study Notes on Data Interpretation For Engineering

Interpretation is the process of making sense of numerical data that has been collected, analysed, and presented. Interpreting data is an important critical thinking skill that helps you comprehend text books, graphs and tables

Majority of questions asked in the Data Interpretation Section are based on the following topics of the Arithmetic Section -

Ratios
Averages
Percentages

If the basics of these topics are clear, attempting DI in the exams becomes comparatively easy.
Now, let us go through the types of DI graphs/charts that you may encounter in the exams -

Pie Charts
Line Charts
Bar Graphs
Tabular Charts
Mixed Graphs
Logical Venn Diagram

We shall now have a look at the types of questions that are asked under these Data Interpretation Graphs -

Consider the following data presented in the bar graph -

Percentage of Students who like different sports in two different years is provided in the following graph. Total number of Students is 1000 for both the years.

Year 2011 and Year 2012

Now the following types of questions may be asked from this data -

1. Sum or Difference based

These are the most basic questions that may be asked in a DI set. For instance,
What was the sum of total number of students who like Badminton and Cricket in bothe the years?

Now for such questions, first find the number of students who like the two sports in the two years -

2011 - Badminton = (12/100) * 1000 = 120

Cricket = (45/100) * 1000 = 450

Total = 570

2012 - Badminton = (20/100) * 1000 = 200

Cricket = (37/100) * 1000 = 370

Total = 570

Sum = 570 + 570 = 1140

2. Averages based Questions

Average based questions are very commonly asked in the Data Interpretation sets. For instance,

What is the average number of students who like badminton, cricket and football in 2011?

Total students who like badminton, cricket and football in 2011 = (12 + 45 + 22) = 79% of 1000

Required average = 790/3

3. Ratio based question

Another arithmetic operation based question that may be asked is Ratio based.
Now, these questions may be asked directly or in combination with above. For instance,

What is the ratio of the students who like football and tennis in 2011 and those who like volleyball and squash in 2012?

Students who like football and tennis in 2011= (22 + 4) = 26% of 1000

Students who like volleyball and squash in 2012 = (10 + 5) = 15% of 1000

Remember for such questions, you do not need to do the entire calculation, because such numbers will eventually cancel out while calculating the ratios.

Required ratio = (26% of 1000) : (15% of 1000) = 26 : 15

4. Percentage based question -

These are yet other arithmetic problems that are usually asked in DI questions.
These problems again may be asked individually or in combination with the sum or difference based problems. For instance,

The students who like badminton and squash in 2011 is what percent of the students who like football and swimming in 2011?

Students who like badminton and squash in 2011 = (12 + 2) = 14% of 1000

Students who like football and swimming in 2011 = (22+7) = 29% of 1000

Here again, do not calculate the entire value.

Required % = (14% of 1000) / (29% of 1000) * 100 = 1400/29%

Same data may be presented in the the form of other graphs as well, however, the approach to attempt the questions would remain same.
You may find numbers in place of percentages or vice - versa, so do read the question carefully before proceeding.

Line Graph

Year 2011 and Year 2012

Tabular Chart

Pie Chart

One more variety of question that may be asked in pie charts is the angle based. For instance,
What is the central angle corresponding to football and volleyball together for 2012?
Angle = (20 + 10)% * 360 = (30/100) * 360 = 108

Logical Venn Diagram

What exactly is Venn-diagram?

These diagrams were given by John Venn. To put simply, these diagrams show all possible logical relationship between a numbers of elements.
In a typical Venn-diagram, usually there’s a use of geometrical figures like Circles, Triangles, Squares & Rectangles.
A basic Venn-diagram has data represented in ‘Circles’.

1. In a country three persons A, B and C live. They are three different persons. This information can be represented as:

Here, we can see that A, B and C are different elements so they’ve represented by different circles.

If we were to represent information in which two elements are intermingled while the third one is different we’ll do that a bit differently.

2. Suppose, we need to convey this: Dog, Animal, Cow.
Now we know that all dogs are animals (clearly no dog is human) so the circle of ‘dog’ will have to be completely surrounded by circle of animal though circle of animal can have some spare space aside from dog as dog isn’t the only animal. Similarly, all ‘cows’ are animals so the circle of ‘cow’ will have to be completely surrounded by circle of animal though circle of animal can have some spare space aside from cow as cow isn’t the only animal. This information can be represented as:

Here, we can see that ‘Animal’ has been represented by a big circle which encompasses the circles for both ‘cow’ and ‘dog. Notice, the circle for ‘animal’ has some spare space as this can contain other types of animals because ‘cow’ and ‘dog’ aren’t the only type of animal.

Types of questions asked in competitive exams:

Finding relationship:

To solve these kinds of questions, we need to have a strong grip on common relationships that exist in the world around us.
Like to define the relationship between Catholics & Christian we need to know that Catholics are the type of Christians hence we can easily conclude that all Catholics are Christian but some Christians will not be Catholics as they will be the other type of Christians.
This information can be represented as:

A typical question might look like this: Dean, Painter, Singer.

We live in a diverse world where people can be multi-talented also people possess just one talent so this info can be represented by 7 categories of people:

a) Who are only Dean

b) Who are only Painter

c) Who are only Singer

d) Who are both Dean & Painter

e) Who are both Painter & Singer

f) Who are both Singer & Dean

g) Who are all Dean, Painter & Singer.

This information can be represented by Venn-diagram as follow: (for reader’s convenience, the different regions have been labeled as named above but in exams, questions aren’t marked this way)

Finding the exact region:

These are the reverse version of the questions discussed above. Here, the diagram with labelled image is given and we’ve to identify the region specifically asked in the question.
For example, an image like below will be given:

Circle S stands for households having a scooter, Circle T stands for households having a TV set,
Circle W stands for households having a Washing Machine, Circle C stands for households having a car.
Find household having both TV set, Car and Washing Machine but not scooter. (Question ends)
Now, if we look closely we can see that four distinct items have been, these 4 distinct items can be seen as:

Now, there are places where only ‘Circle S and Circle T’ meet, such place can be represented in the figure below with ‘orange’ color,
Similarly, the following colors have been used to represent different regions:
- Green = Only (T, W and S)
- Yellow = Only (T and W)
- Purple = Only (W and C)
- Blue = Only (S, W and C)
- Baby Pink = Only (S and T)
- White = Only (S, T and C)
- Light brown = Only (T, W and C)
- Red = All S,T, W and C.

Note: You don’t have to make such colorful representation in the exam. It’s been only colorized to help you visualized the different regions with specific labels.

Now, we have to find household with TV, Washing machine, car but not scooter.
We know that TV = Circle T, Washing Machine = Circle W, Car = Circle C, Scooter = Circle S
So, we have to find where Circle T, W and C meet but not S.
We can clearly see that such region is represented by light brown region which was marked as ‘7’ in the original question figure.

Similar question can be given which represents different elements using different figures like rectangle, triangle etc. as shown below:

Here, Circle represents college Professors, the triangle represents Surgeons and Chemist are shown by rectangle.
Find the area where Surgeons who are Chemists but not Professors are represented.
To find the area representing only Surgeons and Chemists, we need to look for the where ONLY Triangle(=Surgeons) and Rectangle(=Chemist) meet and no sign of Circle(=professor).
Clearly, such area is shown by region marked as Z only (and not Y because that would include Circle also).