CRACKING THE DI (DATA INTERPRETATION) PART OF COMPETITIVE EXAMS - THE FALLACY, HOW TO PREPARE

AND TIPS & TRICKS

 Current Affairs  11:11 PM

Year Sales (Rs. In Lacs)2008 112009 172010 262011 472012 89

The question being asked is "In which year did the company see the highest percentage growth in sales as compared to the previous year?" How will you start? Think before you read thepost below.

Interpreting the Data or Chewing the Data

The cartoon above shows that most of the time we chew the data. By chewing we mean -"most of you would have LITERALLY calculated the percentage growth year-on-year andthe year which shows thehighest percentage growth over the previous year is the answer".  This is what you would've done(approximate values):

Year Sales (Rs. In Lacs) Incremental Sales % Growth overPrevious Year

2008 11 -- --2009 17 6 6/11 = 54%2010 26 9 9/17 = 53%2011 47 21 21/26 = 81%2012 89 42 42/47 = 89%

And hence the answer is 2012.

A) This is the first fallacy in Data Interpretation.

Data Interpretation - The word itself conveys everything. You're supposed to "interpret" the data andnot "blindly chew" it. The data given in the question was easy and hence you could do it quickly.Imagine if the data had been:

Year Sales (Rs. In Lacs)2008 11.3252009 17.8752010 26.4372011 47.8962012 89.776

Would you still calculate the difference between sales (incremental sale) and hence calculate thepercentage growth?

Tips & TricksYOU SHOULD NOT. Because the paper setter wants you to "interpret" the data and hence you'resupposed to calculate it quickly. Here's how you should do it rapidly:

Write all the fractions and see which is the largest (you're not required to calculate itACCURATELY to 2-3 decimal digits) . The fractions are - 17/11, 26/17, 47/26 and 89/47 and the output is:

Fractions in %17/11 = 154%26/17 = 153%47/26 = 181%89/47 = 189%

Let us note two things here:

1.    Although it's not necessary to find percentages at all, it is only done to show that whether you 

compare a year's sale to its previous year directly or whether you find the incremental sale and then 

do this comparison, the result is SAME.

2.      The percentages are EXACTLY greater than 100% than all the corresponding percentages 

because 100% = 1, which is Previous year/Previous year.

How to Prepare for DI:This trick will save time and help you get answers without much calculations.

B) Second fallacy in Data Interpretation

When working with fractions, we have the tendency to find the values of the fractions, when whatessentially we're supposed to do is "compare the fractions".

Tips & Tricks:Data Interpretation is not about calculating the exact values (this is only required when the options are very close). It's about "approximating".

Let us say you're given the fractions: 5/11, 9/13, 5/9 and 7/11 and are asked to find which is the largest of all. There is no need to calculate all the fractions. To find the largest fraction you should know in which fraction is the denominator the least multiple of the numerator. Here are two ways to do it:

1st Way:1. Take 5/11 and 9/13.2. Cross multiply the terms.3. So we have: 5*13 and 9*11 i.e. 65 and 99.4. 99 is greater i.e. 9/13 > 5/115. Now we do for 9/13 and 5/9: 9*9 and 5*13 i.e. 81 and 65.6. 81 is greater i.e. 9/13 > 5/9.7. Now compare 9/13 and 7/11: 9*11 and 13*7 i.e. 99 and 91.8. So 99 is greater i.e. 9/13 > 7/11.9. Hence 9/13 is the largest of all.2nd Way:1. Invert the fractions: 11/5, 13/9, 9/5, 11/72. Now 11/5 > 2 and 9/5 is very close to 2.3. 13/9 = 1.4 and 11/7 = 1.54. Hence 13/9 is the fraction where the denominator is the smallest multiple of the numerator.5. Hence 9/13 is the largest of all.How to Prepare for DI:This trick will not only help in DI but also in Quantitative Ability in competitive exams.

C) Third fallacy in Data InterpretationData Interpretation is ONLY about calculation. This is false. It's also about logic and reasoning.Here's an example:

The total sales are Rs 542 crores and total quantity is 4.231 lakh tonnes. Question is: Whichcountry has paid the highest average price?

A normal person would do the following (let us say for Russia):1. Find 35% of 542 crores.2. Find 18% of 4.231 lakh tonnes3. Find the ratio of (1) and (2) calculated above.And hence the same is repeated for all 4 countries.

Tips & Tricks:Let us say you want to compare Brazil and Russia. You would do:(20% of 542) / (25% of 4.231) and (35% of 542) / (18% of 4.231)

We can see that 542 and 4.231 are common terms in all the ratios.We can just get rid of them. Thank god, wow we're left with:

Brazil 20/25 < 1Russia 35/18 > 1India 40/42 < 1China 5/15 < 1

Hence the answer is Russia.