1. Introduction to Data Interpretation

Data Interpretation (DI) involves interpreting, organising or performing arithmetic operations on given data to arrive at meaningful information and answer the questions asked. We can have data in multiple formats (e.g. tables, graphs, statements, etc.). Sometimes, entrance tests will give us incomplete data (e.g. a partially filled table), and we will use calculations and logical reasoning to get complete data.

DI questions will provide a set of data, usually facts and figures. You may also get tables, diagrams (graphs, pie-charts, etc.) or statements. You need to analyse the given data to answer the questions. Most exams including CAT have cases with data with 2 to 6 questions linked.

Solving DI questions require the use of simple arithmetic operations, as well as logical reasoning. Each and every clue in a DI case is important. Exams such as NMAT and IIFT may provide calculation intensive problems, while CAT focuses more on DI with reasoning.

Examples of DI cases
1) Revenue of companies across time/location/products
2) Summary of survey responses or statistics
3) Qualitative or quantitative product comparisons
4) Physical or geographical data (e.g. rainfall across states, population, etc.)
5) Data about groups or teams (e.g. team scores, goals, etc.)

Key types of mathematical/statistical tools used:
1) Tables: Arrangement of data in rows and columns.

2) Bar graphs: Uses bars or rods to represent various data using the X-axis and Y-axis parameters as scale.

3) Line graphs: Commonly used to show the variation of a parameter over time. An important attribute here is the slope, which shows the change in data w.r.t. time.

4) Pie charts: Circular chart used to represent shares of one item across multiple parties. The total is taken to be 100%. We need multiple pie charts to showcase these.

5) Venn diagrams: Used to represent Set theory problems, where elements may or may not be part of sets/groups.

We have covered these as well as many other formats in this section.

2. Basics of a Table

Tables provide data across rows and columns, and each cell is the intersection of a row and a column. A table is systematic and simple to record and read data. We have been used to tabular representation of data since a young age (e.g. marks of all students in a class, statistical or geographical details of different states, etc.). The spreadsheets that we use, such as MS Excel, are also tables.

A table comprises of
Columns & their Headers: A column is a vertical set of values in a table. The headers of the columns are typically titles written at the top (i.e., the top-most or first row).

Rows & their Headers: A row is a horizontal set of values in a table. The headers of the rows are written at the left (i.e., the left-most or first column).

Cells: A cell contain a value that falls under the particular Row and Column headers the cell is under.

Totals: When we have a data table containing numbers, it is very important to write the totals (where data is an absolute number and not a percentage or proportion). In fact, writing the totals is a key step in solving most DI cases with tables. Column totals are written in the bottom-most row and the row totals are written in the right-most column. The grand total (sum of all cells, which also equals sum of all the row totals and sum of all the column totals) is written in the bottom-right corner of the table.

2.1 When do we present data in a table?

When each data point or number would have exactly 2 attributes, then a table can be drawn such that 1 of the attributes is the heads of the columns while the other is the heads of the rows.

For instance, the table below contains the revenues of 4 companies (which are given in the first column) over 3 years (which are given in the first row). The right-most column contains the total revenue of each company over 3 years and the bottom-most row contains the total revenue of all 4 companies for each year.

Also note the top left cell which states that all the figures mentioned in the table are in Rs. Crores.

Each cell inside the table pertains to a company and a year. For instance, Rs. 400 crores is the revenue of Bravo Plc in 2022 and Rs. 600 crores is the revenue of Delta Co. in 2021.

Note: In cases where each person or data point might or might not have certain attributes, we use Sets/Venn Diagrams to solve them.

3. Solved Examples

In this lesson we will look at Data Tables, which seem to be calculation intensive. Most of the questions would involve the use of Arithmetic Operations, percentages, averages and ratios to find the answers.

Note that when a table contains numbers that run into tens of thousands, we might assume it would be calculation intensive and would require accurate answers. This results in a tendency to skip these cases. However, when it comes to aptitude tests, you would not be expected to crunch these big numbers as they are.

If such a case requires calculations, you can use approximations (refer Example Cases 3 & 6). Or in the cases such as the following, where the number of passengers run into tens of millions, there are no calculations. Therefore, when you see huge numbers, do not skip the case immediately. Instead, take a look at the questions and then decide whether you should attempt the case or not.

Example Case 1

Directions for questions 1 to 4: Answer the questions based on the table given below concerning the busiest 20 international airports in the world.

[CAT 2001]

1) How many international airports of type ‘A’ account for more than 40 million passengers?

(1) 4
(2) 5
(3) 6
(4) 7

2) What percentage of top ten busiest airports is in the United States of America?

(1) 60%
(2) 80%
(3) 70%
(4) 90%

3) Of the five busiest airports, roughly, what percentage of passengers is handled by Heathrow Airport?

(1) 30
(2) 40
(3) 20
(4) 50

4) How many international airports not located in the USA handle more than 30 million passengers?

(1) 5
(2) 6
(3) 10
(4) 14

Solution

1)

Cities whose passengers are greater than 40 million and have type 'A' airport are Hartsfield, Chicago-O'Hare, Los Angeles, DFW, and San Francisco.

This gives us a total of 5 international airports.

Answer: (2) 5

2)

Of the top 10 busiest airports, a total of 6 airports which belong to the USA.

$\dfrac{6}{10} \times 100 \%$ = $60 \%$

Answer: (1) 60%

3)

Total number of passenger handled by top 5 busiest airports (taking nearest value in millions) = 78+73+64+62+60 = 337. Passengers handled by the Heathrow airport (taking nearest value in millions) = 62 . $\dfrac{62}{337} \times 100 \% = 18.39 \%$, approximately 20%.

Answer: (3) 20.

Alternatively,

By observation, we know that passengers from the top 5 are closest to each other, and answer options are far apart.
$\dfrac{1}{5} = 20%$

4)

All the 20 airports have more than 30 million passengers. Remove the airports that lie inside the USA. The airport ranked 4,6,7,8,11,18 are outside of USA. This gives us a total of 6 airports.

Answer: (2) 6

Answers:
1) (2) 5
2) (1) 60%
3) (3) 20
4) (2) 6