Basics of Data Interpretation
Data Interpretation accounts for a major chunk of questions in common aptitude test format. Mastering this area is comparatively less tiresome than the other two major sections, Quantitative Aptitude and Verbal Ability. Data Interpretation tests our ability to understand and apply data. Usually DI won’t challenge us with complicated stuffs. Given enough time we can solve most of the Data Interpretation questions with good accuracy. But Data Interpretation lures us in to its web by giving seemingly harmless questions with hidden traps such as unwanted data and unnecessary calculations. If we do not approach DI smartly, we will waste our time.
Some best practices while dealing with Data interpretation are
- Be clear on what is given and what is asked.
- See how much effort is required to get the required data from the given data.
- if a question demand unreasonable efforts, LEAVE those questions and come back if possible.
- Focus only on useful data
- Never lose your heart if you see lot of data. Until you are able to comprehend the given data, you are good to go.
- Do ONLY what is required. Don’t try to keep data ready before solving!
- Approximate wherever possible.
- If only relative values are asked, don’t calculate the actual values.
Rather than going on and on with theory we will try to understand these concepts by solving some Data Interpretation questions. Here we go.
The table below reports annual statistics related to rice production in selected states of India for a particular year. (CAT 2005)
1.Which two states account for the highest productivity of rice (tons produced per hectare of rice cultivation)?
(1) Haryana and Punjab (2) Punjab and Andhra Pradesh
(3) Andhra Pradesh and Haryana (4) Uttar Pradesh and Haryana
2. How many states have a per capita production of rice (defined as total rice production divided by its population) greater than Gujarat?
(1) 3 (2) 4 (3) 5 (4) 6
3. An intensive rice producing state is defined as one whose annual rice production per million of population is at least 400,000 tons. How many states are intensive rice producing states?
(1) 5 (2) 6 (3) 7 (4) 8
What is given?
Data is represented using a quantitative method (Table).
Given Data are:
Total area available
Area used for rice cultivation (as % of total area)
What is asked?
Rice productivity = tons produced per hectare of rice cultivation
Per capita production of rice = total rice production divided by its population
Intensive rice producing states = annual rice production per million of population is at least 400,000 tons (0.4 million tons)
What is the effort required?
We need to find out the area under rice cultivation in hectares as the given data is as % of the total area. Options have only 4 States in them (Haryana, Punjab, Andhra Pradesh and Uttar Pradesh). Hence, we need to find area under rice cultivation in hectares ONLY for four states.
We need to find the number of states Per capita production of rice is greater than Gujarat.We may not have to calculate the actual value as we are asked to find out whether the value is higher or lower than a given reference point (of Gujarat’s).
Here also we may not have to find the actual values as we are asked to find out the values higher than a reference point (400,000 tons).
Total Area under rice cultivation (in million hectares) for the required 4 states
Haryana: 4 * 80/100 = 3.2
Punjab: 5 * 80/100 = 4
A.P: 28 * 80/100 = 22.4
U.P: 24 * 70/100 = 16.8
Rice production in ton per hectare for the required four states
Haryana: 19.2/3.2 = 6
Punjab: 24/4 = 6
A.P: 112/22.4 = 5
U.P: 67.2/16.8 = 4
Hence Haryana & Punjab account for the highest productivity of rice.
Here trap that is we may start finding out the area under rice cultivation for all the states rather than the required four. Never jump to solution before understanding what is really required to solve the questions.
We are asked to find the number of states with Per capita production of rice higher than Gujarat.
Per capita production of rice for Gujarat:
X = 24 / 51 = (20.4 + 2.04 + 1.02 + 0.51 + …)/51 ≈ 0.4 + 0.04 + 0.02 + 0.01 ≈ 0.47
This is a neat trick while solving fractions. Concept is simple. Write numerator as a sum or difference of numbers which can be written in terms of denominator. In the above expression, 24 is written as sum of 20.4 (51 * 0.4), 2.04 (51 * 0.04), 1.02 (51 * 0.02) and 0.51 (51 * 0.01).
Coming back, we got Per capita production of rice for Gujarat, say X = 0.47 ≈ 0.5
We need to find states where
Production / Population > 0.5
= > Production > 0.5 * Population
= > 2 * Production > Population
If the Population is less than or equal to double the Production, per capita production of rice for that state will be higher than X.
If the Population is considerably more than double the Production, Per capita production of rice for that state will be lesser than X.
If Population is only little more than double the Production we may need to solve for actual value (as we approximated)
We can easily find out that 3 states (Haryana, Punjab and A.P) have its Per capita production of rice higher than Gujarat. For Maharashtra we may not be able to easily compare with the reference value. So we need to solve only that one.
Per capita production of rice for Maharashtra
48/97 ≈ (38.8 + 4.85 + 3.88 + …)/97
≈ 0.4 + 0.05 + 0.04 ≈ 0.49 which is greater than X (0.47)
Hence four states (Haryana, Punjab, A.P and Maharashtra) have Per capita production higher than Gujarat.
We didn’t find the actual per capita production for all states. We just checked whether the values are above or below the reference point. Only in case of closer values we solved using approximation. Here if we spend time to find all the actual values it would have been a terrible waste of time, which was the hidden trap.
Here we need to find states whose annual rice production per million population is 400,000 tons (0.4 million tons) or more. In this case also we are asked to find out relative values based on a reference value (greater than 0.4 million tons/million population). We don’t have to solve for actual values.
Production/Population > 0.4
= > Production/0.4 > Population
= > Production * 2.5 > Population
we need to identify states where Production * 2.5 > Population.
We can get the status for all the states without doing any complex calculation.
May be we need to do some quick check for U.P
67.2 * 2.5 = 60 * 2.5 + 7 * 2.5 + 0.2 * 2.5
= 150 + 17.5 + 0.5 = 168 > 166, Hence YES.
We have eight states which qualify as intensive rice producing states.
By converting division by 0.4 to comparatively easier multiplication with 2.5 we were able to find the relative values much quicker. If we go with the conventional approach of solving each fractions and calculating the actual values we will end up spending lot of time and chances are more that we mess up with our calculations, another trap.
Just imagine that we had one more question to find the state ranked at number five among the top intensive rice producing states with one among the option as ‘None of these’. Here, we need actual values and we cannot limit the calculations based on options as one option is ‘none of these’. We know how to solve this question but it is better to leave it and come back if we are left with some time and no better question remaining.
Another important aspect in Data Interpretation is qualitative analysis. We will solve one from that bucket too.
Answer the questions on the basis of the data presented in the figure below.
(CAT 2003 Retest)
1. During 1996-2002, the number of commodities that exhibited a net overall increase and a net overall decrease, respectively, were
(1) 3 and 3 (2) 2 and 4 (3) 4 and 2 (4) 5 and 1
2. The number of commodities that experienced a price decline for two or more consecutive years is
(1) 2 (2) 3 (3) 4 (4) 5
3. For which commodities did a price increase immediately follow a price decline only once in this period?
(1) Rice, Edible oil, and Dal
(2) Egg and Dal
(3) Onion only
(4) Egg and Onion
What is given?
Data is represented using a Qualitative method (Line graph). Given data are
Price of commodities from year 1996 to 2002
Trend of commodity price during the tenure 1996 – 2006
What is asked?
Net overall increase/decrease of commodities during the period
Trend in price fluctuations
Question 2 & 3 are purely qualitative in nature. Visual inspection can yield the answer. Both are very much doable and can fetch us some easy marks.
Question 1, we have to find the net increase/decrease of price for the period. We can either approach it using conventional quantitative methods or can use a qualitative approach. If the qualitative approach crossed your mind by now, it’s all yours... else don’t waste time in this one unless you don’t have an easier question left to do.
As a matter of fact, you don’t have to touch your pen to solve all the three questions.
By visual inspection, answer is five. Except for edible oil all other commodity price decline for two or more consecutive years during the tenure. We need to find the pattern of 2 continuous dips in the graph for the commodity during the period.
This question needs us to find the commodities which has a price decline followed by a price increase and only once. We need to find a particular pattern in the plot which is a dip and rise coming together and only once. A Dip-Rise together makes a V shaped plot. Hence we are asked to identify those commodities whose plot has one and only one V in it.
Before start solving, we will see another important aspect here. Options are there for helping us. Not just the right one, but all options! Build the habit to bring down the calculations to the minimum and do only what is really required. Less calculations means lesser time required and lesser chance for committing mistakes
Carefully observe the options to see whether there is any chance to simplify our efforts. Here Option 3 needs us to find the pattern only for one commodity (Onion). The trick here is that if Onion satisfies the condition, then we can eliminate options 1 and 2 as Onion is not there in both of them. Otherwise if Onion does not satisfy the condition then we can remove option 3 and 4 as Onion is included in them.
Onion has one V and only one V in its plot. Option 1 and 2 out from our attention.
Now to mark between option 3 and 4 we need to take the plot of Egg. We have one and only one V in egg plot too... hence option 4 is the right one.
Many mistakes we commit during our aptitude exam is not mathematical, it is psychological. By using best method or not, it is relatively easy to solve the 2nd and 3rd questions in this set. Once we get those two questions into our basket it is natural to urge to ‘Conquer’ the whole set by solving the first question. First question is also easy if we got the correct approach. Otherwise we are in loss in terms of time.
We are asked to find the net increase/decrease in the overall price in the period. There is no optimisation available as we need to find the status of all the commodities to get the answer.
We can go with the quantitative method, like
Rice price fluctuation during the period: 10 - > 14 - > 13 - > 10 - > 11 - > 12 - > 14
Net price difference = +4 – 1 – 3 + 1 + 2 + 2 = +4. (Hence net is positive)
If we do this for all the commodities and for all the years, we will find 42 values from the graph, calculate the difference between previous data and then find the net value... ouch!
While discussing number line we shared a concept. If a we take 100 steps forward and then 99 steps backwards in a number line it is effectively taking only one step forward. Same applies here. We are asked to get the net value of price difference during the period. Just take the difference between initial and final point of the plot for each commodity. If final point is above the initial point, net is increase. If final point is below the initial point, net is decrease. Visual inspection will suffice. Edible oil and Dal has a net decrease and other four show a net increase. Hence option 3.
Data Interpretation is an approach based section than a syllabus based one. If we don’t treat Data Interpretation carefully, DI will treat us bad, waste our time and trick us into an awful situation where we have doable questions remaining with no time left to solve them. There is not much theory to learn but mastering DI comes through practice. It is perfectly OK to take some time to pick up the DI skills. The focus while building your Data Interpretation skills should be on your ability to spot the right questions and pick the best approach quickly.