Data Interpretation is one of the easy sections of one day competitive Examinations. It is an extension of Mathematical skill and accuracy

By Dipak Mishra

Data Interpretation is one of the easy sections of one day competitive Examinations. It is an extension of Mathematical skill and accuracy. In the CSAT scenario, it has become important because more often than not, the civil services officers have voluminous data in different forms, from which they are required to churn out information and help the concerned authorities in formulating policy decisions.

Data Interpretation tests your speed, decision making capability and analysing data. It consists of a good number of graphs, charts and tables from which you will have to analyse data. The key to cracking this area is to quickly identify the key pieces of data that you will require to work on the questions asked. It is not unknown for question-setters to try and bewilder students with a large amount of data, most of it unnecessary. As a rule, the more the data presented, the easier the questions that follow, so don’t lose heart if you see a table with 10 columns occupying one whole page. On the other hand, several seemingly innocuous questions may stump you.

**Different Data Forms**

The different data forms that usually confront the students are

**Table Graphs **

Tables are often used in reports, magazines and newspaper to present a set of numerical facts. They enable the reader to make comparisons and to draw quick conclusions. It is one of the easiest and

most accurate ways of presenting data. They require much closer reading than graphs of other forms and hence are difficult and time consuming to interpret.

One of the main purposes of tables is to make complicated information easier to understand. The advantage of presenting data in a table is that one can see the information at a glance.

**Pie Charts **

They derive their name from its shape, like that of a pie divided into various portions. They always represent data in the form of a percentage of the total, with the total percentage being 100. In such a chart, the length of the arc (and therefore the angle each sector subtends at the centre) is proportional to the quantity it represents. Such charts are often used in the corporate world and in newspapers. Since a circle comprises 360 degrees, each percent of a pie-chart is equal to 360 divided by 100, or 3.6 degrees. This fact will be important for the calculations you are expected to perform.

**Bar Graphs **

Bar graphs represent data in the form of columns or bars. Bar graphs can be horizontal or vertical. The length of the bar is proportional to the data value represented by it.

**Line Graphs **

Line graph represents data in the form of straight lines that connect various data values. Both line graphs and bar graphs are used to convey same things and hence can be used inter-changeably. For example, a line graph can be generated by joining the tip of the bar graph.

**Caselets**

In caselets, the mathematical data is represented in the form of a paragraph. Hence extracting data and establishing relationships between different data values becomes difficult. However caselets are very popular with the examiners.

**Combined Data Sets **

Data is represented in two or more different types of data sets. It could be combination of a table and a graph or two or more similar graphs. You may have to correlate the data in different data sets to solve these questions. Thus interpreting data takes time. These type of sets are very commonly asked. However based on experience, we feel that that if such a set comes in CSAT, then it would not be heavy on data and be an easy set to interpret with the focus on correlation of data.

**Some tips to score well in Data Interpretation:
Careful Reading and Analyzing
**

The first and the most important step in solving any Data Interpretation question is to read the question carefully. Many a times, the data given below the graph turns out to be more important than most of the numbers in the graphs.

The next step should be to analyze the given graph/data carefully. Do not try to see the questions first and find out the answers accordingly. You will waste your time if you follow that method. Try to understand the graph. Instead do the reverse.What is the graph all about? Which years does it cover? Is the data in absolute terms or in percentage terms? What do the two axis signify?, etc. Look at the statistics for each graph, chart, table or pie diagram. Look carefully at the labels. Make sure you understand the central theme of the data.

**Worry less about data given**

Understand the question, which might contain lots of data that is unrelated and 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 below the graphs. But, if you were 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. Don’t get disheartened by the amount of data and the only thing important is whether you can correlate the data between the graphs properly.

**Skip Calculative Questions **

Some questions require lots of calculation in order to be solved. These questions are known as the speedbreakers. Such questions are best left alone, at least in the first round. Once you have solved all the easy questions then go to the difficult ones. If you try such questions in the first round, you will lose your precious time on them and may not be able to attempt some simple questions that may follow. Also there are many unnecessary calculations that we do, which might 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.

**Attention to the minor details**

This is related to the first step which we discussed. Sometimes, the questions will use a different unit for the question and another unit for the data. For example, the data given may be about sales volume in Millions. However, the question may ask about sales volume in lakhs. Also you should have an idea about sales volume and sales value.If you do not pay close attention to the unit, you may chose the wrong answer.

Sometimes there are questions which will ask us to find out some data for which information may not be available. 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. We will look into this in our next part of discussion.

**Approximate properly**

CSAT is not about finding the exact answer always. Most of the times, the options given are far enough from each other to give you enough room for approximation. So, for example, if you are asked to divide 642678/161335, you can easily approximate that the answer will be somewhere around 4 by looking at the first 2 numbers only. 64/16 is 4. So, instead of dividing it and finding the accurate answer, try to find an appproximate 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.

Lets attempt one set and try to apply those steps

The pie chart shows the distribution of Rs 6 lakhs spent by a construction contractor on different items.

1. The amount spent on cement is

a. Rs.2,00,000

b. Rs.1,60,000

c. Rs.1,20,000

d. Rs.1,00,000

Total is Rs. 6,00,000 (=360 degrees of the circle).Cement is 72 Degrees.

Apply the ratio principle. Hence 72/360= M/6 lakhs where M is the amount spent on cement. HenceM=(72*6)/360=1.2 lakhs.

2. The amount spent on labour exceeds the amount spent on steel by

A. 5% of the total cost

B. 66.66% of the total cost

C. 12% of the total cost

D. 15% of the total cost

There is no need to find absolute values. Just observe the degrees. The difference between Labour and Steel is 90-54 or 36 degrees. And total cost is (6 lakh=) 360 degrees.

So the percentage= 36/360 x 100 =10% of the total cost. But if the options would have omitted the word “of the total cost”, then the answer would have been (90-54)/54 × 100= 66.66%.The base would have been the cost of steel, in that case.Notice the wrong option B to create confusion in the mind.

3. The amount spent on cement and steel is what percent of the cost on supervision?

A. 70%

B. 42.94%

C. 50%

D. 233.33%

Again no need to find absolute values. Just observe the degrees. The total degrees is 126 on cement and steel while it is 54 for supervision. It is asking, “what percent of the total cost on supervision?”

So cost of supervision is the “base”%.. Hence the required value=(126/54) x 100 =233.33%.

If we reverse the base(take the base as cement and steel) , it becomes 42.94%. If we take the total cost as the base the value becomes 126/180 x 100=70%.If we take the total cost of three items vis-à-vis the total cost as the base, then the value becomes 180/360 x 100=50%.These are the 4 options given in the question as observed here.

**DATA SUFFICIENCY**

Data sufficiency tests your skill on the amount data you require to take a decision. Quite a number of times, you may have to arrive at a decision on the amount of data available, which might be more /less than you actually require. If you ask your block officer under you as to “ How many families have 2 or more girls in this area” and he/she starts reeling off figures of the population of the block according to last census, infant mortality rate, families having children, population growth etc..that will not serve your purpose. The focus should be only on girl child and not children. A family can have girls and boys, but the question asks” How many families have 2 or more girls in this area”. That family can have boys, but whether it has 2 or more girls should be the aim that you should focus on.

**Format of Data sufficiency question**

The format of the question would be something like this.

1. Is integer x positive?

1. x > 9

2. x2 > 81

Mark

(A) if one statement alone but not on other statement alone is sufficient to answer the question

(B) EACH statement ALONE is sufficient to answer the question asked

(C) Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

(D) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Data Sufficiency questions hinge on whether a statement is sufficient to answer a question. A statement is sufficient when it guarantees exactly one answer to that question. For example, in the question:

Is integer x positive?

The statement “x > 9” would be sufficient, as any number greater than 9 is also greater than 0 and therefore positive.

The statement “x2 > 81”, however, would not be sufficient, as there are two potential values of x: 9 (which gives the answer “yes, x is positive”) and -9 (which gives the answer “no, x is not positive”). The correct option is A.

Your job, then, is to determine when a statement is sufficient to provide exactly one answer to the overarching question.

**Some tips to score well in Data Sufficiency:**

**Don’t solve the question. **

Data Sufficiency questions simply ask whether you COULD solve the question given the information in the statements. Don’t waste valuable time actually solving unless you are uncertain of sufficiency! Data sufficiency questions are not supposed to involve long and drawn-out calculations. If you find yourself calulating, there is probably something you’re not seeing. Remember that variables can equal a variety of values: negatives, positives, integers, fractions, zero. Don’t simplify when you don’t know what a variable can equal, and don’t assume variables are positive integers!

**For “yes/no” questions, focus on whether you are getting a firm yes or no.**

There is no “correct” answer. Our task is merely to determine when we have enough information. It is possible for one statement to answer the question “yes” and the other to answer the question “no” and have BOTH statements be independently sufficient.

**Focus on this question**

2. Is x=4?

1.X3= -64

2.X2=9

Mark

(A) if one statement alone but not on other statement alone is sufficient to answer the question

(B) EACH statement ALONE is sufficient to answer the question asked

(C) Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

(D) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Here from the 1st statement we get X=-4 which answers the question that X IS NOT 4.

The 2nd statement shows that X is either 3 or -3 and hence not 4.Hence X IS NOT 4.The correct option is B. Note that NO is also an answer to a question.

**Note down the variables needed for answering the question BEFORE looking at the statements.
**

Try to write down your own prediction first. It helps you to eliminate the statements more quickly if you have something to compare their information to, and forces you to spend more time thinking critically. Don’t rush this step!

**Remove biasness in mind. **

Once you determine the type of question and have analyzed the information given, analyze the first two statements independently of each other. If you have used Statement 1 to answer the question, try to “forget” statement 1 when you move on to statement 2. Don’t underestimate how challenging this can be – try not to mentally “carry over” any info from one statement to the next.

**Use the process of elimination to narrow down the choices methodically.**

If Statement 1 is sufficient, eliminate C and D. The only two options are A and B. Conversely if 1 is NOT sufficient, eliminate B. Simply by appropriately analyzing the first statement, you can eliminate two answer choices! If statement 1 is challenging for you, you can start by analyzing statement 2. If statement 2 is insufficient, then choices B can immediately be eliminated. It doesn’t matter which statement you analyze first, as long as you start by looking at them individually. Also in some , the question itself gives some of the information which you require. It might be possible that same information is rephrased and again given in one of the statements. You should reach this conclusion that “THE STATEMENT IS REDUNDANT”, and do not use that statement to answer the question.