## Data Interpretation

Theory

Data Interpretation is one of the least liked sections of CAT by most students. The copious amount of calculation involved puts off even the most diligent of students. Again, this is one of those subjects where students can dramatically improve their scores by putting in some practice. But don’t just solve the entire set by force, put in some smart work. Learn the tricks of approximation and calculation given above and put them to use every time you solve a set. The crux of doing well in Data Interpretation is accurately solving in less time. Most of the students are able to understand what is asked and how to do it. The only difference between a high scorer and a low scorer is accuracy and speed. As most of the questions are interrelated (as in the data derived from one is used by another) these errors can get compounded during the exam. Make sure you spend enough time accurately solving those questions where the data derived will be used by the other questions. Use the techniques given above to improve you time, but be cautious of over approximating. Approximating 1729 to 1700 is very different from approximating 17 to 20.

Tip

### Averages:

• In case you have to calculate the average of a group of numbers (for eg marks) which are distributed around some round number. For example to find the average of 94, 97, 92, 89, 84 and 99. These numbers are distributed around 90. Find the difference of these numbers as compared to 90 and take and average of that number. Hence we calculate the average of 4, 7, 2, -1, -6 and 9 ~ 15/6=2.5. Hence the average of marks = 90+2.5=92.5
Formula

### Rate of Growth:

• Provided r the rate of growth for n years, we can approximate it as follows: By binomial theorem $$(1+x)^{n}$$ = 1 + nx + $$\frac{n(n-1)}{2!}x^{2}$$ + $$\frac{n(n-1)(n-2)}{3!}x^{3}$$...
• If nx<10%, we can approximate this to 1+nx. Else, approximate to the third term.
• If we are given the value after n years of r rate of growth and asked for the earlier value. Here n will be negative in the formula given above
• Suppose p was the value in 2009 and after 2% growth for 3 years we get 100 in 2012. Hence $$p$$ = $$\frac{100}{(1+2\%)^{3}}$$. We can approximate this to p=100(1-3*2%+((-3)(-4)/2!)*0.04%)=100(1-6%+6*0.04%)=94.24. The actual value is 94.232, which is very close to our answer.
Tip

### Approximation:

• Read the options before deciding on the amount of accuracy of calculation needed. If the options are fairly far apart, you can approximate while calculating
• Beware of over approximation. Approximations (especially if you always round down or round up) can have a cumulative effect and make the answer you get very different from the actual answer
• Be mindful of the direction of your approximations. If you always round down a fraction, the answer in the option should be slightly higher than the answer you get
• Division: For eg you are calculating the fraction 1329/713. From the first look we can say that this fraction is less than 2 but close to 2. 713 does not seem to have any obvious factor like 2,3, 5 etc to cancel off. To calculate the result we can round down to 700 by removing 13 from the denominator. 13 is around 2% of 713. Hence reducing numerator also by 2% we get 1329*2%~26. Hence the ratio is approximately 1303/700 =1.861. The actual value is 1.8639 which is fairly close to what we got.
• Ratio Comparison: Suppose you have to compare the following ratios 1129/1254,1249/1324 and 1449/1499. All three numbers are less than 1. Comparing 1129/1254 and 1249/1324. We know that (a+x)/(b+x)> a/b if x is positive and a/b<1. Hence 1129/1254 < (1129+70)/(1254+70)=1199/1324. Hence 1129/1254 < 1249/1324. Similarly,1249/1324 < (1249+170)/(1324+170)=1419/1499. Hence 1249/1324 is less than 1449/1499
Tip

### Graphs:

• In case numbers are not given adjoining bar graphs, column charts, pie charts etc, write them down paper before proceeding. It reduces the chances of error by incorrectly reading a graph in the midst of solving a problem