Introduction to Data Interpretation – MBA CUET PG

Introduction

Data refers to a collection of observations, measurements, or facts related to any physical, social, or economic event. It may be presented in the form of numbers or descriptive statements.

Data Interpretation is the process of organizing, summarizing, and analyzing data in order to extract meaningful information. In this process, large sets of raw data are arranged into clear and concise forms such as tables, graphs, pie charts, and other visual formats. These organized presentations make it easier for students to understand the data and draw accurate conclusions.

Data Interpretation questions are designed to test a student’s speed, comprehension, analytical ability, and decision-making skills.

Basic tools required for solving Data Interpretation problems include:

• Calculations

• Percentage

• Ratio

• Average

1. Calculation:

Below are some essential tools which help in faster calculations. Students must learn these by heart as much as they can:
(i) Tables
(ii) Squares and Cubes
(iii) Square roots & cube root
(iv) Reciprocal Values

2. Percentage:

Percentage means every hundred. It is a ratio with base of 100. Percentage calculation is the most important aspect in the representation as well as in the interpretation of the data. Students must know about various basic properties of percentage and tricks involved in the faster calculation of percentages.

Some important formula:

Percentage Increase:

$$\text{Percentage Increase}=\frac{\text{Final Value} – \text{Initial Value}}{\text{Initial Value}} \times 100$$

Percentage Decrease:

$$\text{Percentage Decrease}=\frac{\text{Initial Value} – \text{Final Value}}{\text{Initial Value}} \times 100$$

Quantity I is how much percent of Quantity II:

$$\frac{\text{Quantity I}}{\text{Quantity II}} \times 100$$

Quantity I is how much percent more than Quantity II:

$$\frac{\text{Quantity I}-\text{Quantity II}}{\text{Quantity II}} \times 100$$

Quantity I is how much percent less than Quantity II:

$$\frac{\text{Quantity II}-\text{Quantity I}}{\text{Quantity II}} \times 100$$

Students must learn by heart the fractional values of some important frequently used percentages:

$$10\%=\frac{1}{10},\quad 20\%=\frac{1}{5},\quad 40\%=\frac{2}{5},\quad 50\%=\frac{1}{2},\quad 60\%=\frac{3}{5}$$

$$75\%=\frac{3}{4},\quad 80\%=\frac{4}{5},\quad 120\%=\frac{6}{5},\quad 125\%=\frac{5}{4},\quad 150\%=\frac{3}{2}$$

Fractional values of some important frequently used fractional percentages:

$$33\frac{1}{3}\%=\frac{1}{3}$$

$$16\frac{2}{3}\%=\frac{1}{6}$$

$$14\frac{2}{7}\%=\frac{1}{7}$$

$$12\frac{1}{2}\%=\frac{1}{8}$$

$$11\frac{1}{9}\%=\frac{1}{9}$$

$$9\frac{1}{11}\%=\frac{1}{11}$$

$$7\frac{1}{7}\%=\frac{1}{14}$$

$$6\frac{1}{4}\%=\frac{1}{16}$$

$$8\frac{1}{3}\%=\frac{1}{12}$$

$$6\frac{2}{3}\%=\frac{1}{15}$$

Students can also learn some other percentages based on the above tables:

For example:

$$\frac{1}{20}=5\%$$

$$15\%=3\times 5\%=3 \times \frac{1}{20}=\frac{3}{20}$$

$$66\frac{2}{3}\%=2\times 33\frac{1}{3}\%=2\times \frac{1}{3}=\frac{2}{3}$$

$$37\frac{1}{2}\%=3\times 12\frac{1}{2}\%=3\times \frac{1}{8}=\frac{3}{8}$$

Note: If the percentage value is increased by 100%, then the equivalent fraction value will also be increased by 1.

For example:

$$25\%=\frac{1}{4}$$

$$125\%=1+\frac{1}{4}=\frac{5}{4}$$

$$33\frac{1}{3}\%=\frac{1}{3}$$

$$133\frac{1}{3}\%=1+\frac{1}{3}=\frac{4}{3}$$

$$108\frac{1}{3}\%=1+\frac{1}{8}=\frac{13}{12}$$

$$83\frac{1}{3}\%=\frac{5}{6}$$

Must know:

If any quantity doubles itself then it is 200% of its previous value.
If any quantity triples itself then it is 300% of its previous value.
If any quantity becomes 5 times of itself then it is 500% of its previous value.

But

If any quantity doubles itself then it is increased by 100%.
If any quantity triples itself then it is increased by 200%.
If any quantity becomes 5 times of itself then it is increased by 400%.

Note:
Always break the single percentage into easier percentages wherever possible.

For example:

$$65\%=50\%+10\%+5\%$$

$$95\%=100\%-5\%$$

$$45\%=50\%-5\%$$

$$87\frac{1}{2}\%=100\%-12\frac{1}{2}\%$$

$$43\frac{1}{3}\%=50\%-6\frac{2}{3}\%$$

3. Ratio:

It is defined as the reduced form of values of quantities to lowest integers for the purpose of comparison between the values of quantities. It is the result of value of one quantity divided by another. Ratios can be expressed as fractions, decimals or even as percentages. It is necessary that the two figures compared should have the same characteristics and should be expressed either in same unit or in comparable units. For the calculation of ratios, students must learn tables, divisibility of numbers and simplification of expressions etc.

$$\text{Ratio}=\frac{\text{Quantity I}}{\text{Quantity II}}$$

4. Average:

It is defined as the central value of values of all the quantities taken into consideration. It is the result of sum of values of all the quantities divided by the number of quantities. Average is always between the highest and the lowest values among the values of all the quantities. It is necessary that the quantities taken in consideration should have the same characteristics and should be expressed either in same unit or in comparable units. For the calculation of averages, students must learn the various properties related to average.

$$\text{Average}=\frac{\text{Sum of values of all quantities}}{\text{Number of quantities}}$$

Important Points to Remember:

1. Read the question carefully: The first and the most important step in solving any Data Interpretation question is to read the question carefully. You should read all the data that comes with the graphs or table in the question. Many a time the data given above/below the graph (additional instructions) turn out to be more important than most of the numbers in the graphs.

2. Analyze the data carefully: The next step is to analyze the given graph/data carefully. Do not try to see the question first and find out the answers accordingly. You will waste your time following that method. Try to understand the graph. Look at the type of data given in each graph, chart, table or pie chart. Look carefully at the labels.

3. Don’t worry about too much data: Try to understand the question. Sometimes, the question contains lots of data that is unrelated and is not required for answering the questions. When you look at the question you may get discouraged by the lengthy tables or by the amount of information given above/below the graphs. But if you try to understand what the data is about and then look at the question, you may find that you only have to use part of the data.

4. Learn to skim through data: Some graphs have a lot of data associated with them and not all of which is required to solve the questions. Skimming through the data and avoiding mess is an important part of the process. So, just focus on what is required in the question, rather than on all the data at one time.

5. Avoid unnecessary calculations: We have a habit from our school days to solve questions in a step by step method. This is a very good habit for school exams but a really bad habit when it comes to the competitive exams. There are many unnecessary calculations that we do while attempting the questions which cost us a precious few seconds per question. Sometimes, there are many steps that can be skipped but we still do it as we are trained to solve in a step by step method. Learn to skip those steps.

6. Learn to approximate: You do not need to calculate the exact answer for every question. Many a times, the options given are far enough from each other to give you enough room for approximation. So, instead of finding the accurate answer, try to find an approximate answer. This will give you the correct answer more often than not. If however, the options are close, you will still be able to eliminate 1 or 2 options easily.

7. Pay close attention to the units used: Sometimes, the questions may use a different unit for the question and another unit for the data. If you do not pay close attention to the unit, you may be ended up choosing the wrong answer. Always convert the units into the ones which are asked in the question.

8. Skip questions that need too much calculation: Some questions ask too much from you. They require lots of calculation in order to be solved. These questions are known as the speed-breakers. Such questions are best left alone, at least in the first round of attempt. Once you have finished solving all the easy questions and still have time left for the section, you should attempt these questions. If you try such questions, you will lose your precious time on them and may not be able to attempt some simple questions that may follow.

9. Don’t assume anything: Sometimes there are questions which need to find out some data which cannot be calculated even with the help of the data given in the graph and the question. Always be alert enough to see whether the data given is enough to answer the question or not and do not go forward with answering the questions based on assumptions. Sometimes, ‘cannot be determined’ can also be the correct answer.