For anyone attempting the CAT, or any other entrance exam like the XAT, IIFT Entrance, etc., what's the one key word that you absolutely must know? Percentile! CAT Toppers and scorers always talk about the percentile they scored in CAT and mocks. B-schools too have minimum qualification percentiles. If you haven't scored above a whopping 99 percentile, you probably won't make it to the IIMs of the world. But if you are just beginning your CAT prep, this "percentile" is a pretty confusing term, right? How is percentile different from percentage? How do you calculate it? And what does it all mean? In this article, we decode "percentiles" for you!
You probably have questions like:
What are percentiles,
How are they calculated,
Why is your percentile isn't anywhere close to the average of the percentile received in all the sections put together.
Let's look at these points one by one:
1. What is percentile?
Percentile is statistically defined as:
"Each of the 99 intermediate values of a random variable which divide a frequency distribution into 100 such groups. So, if there is a group of 10,000 people, one percentile units would mean 1 percent, or 100 people."
If you assign a rank to all of these individuals, from 1 to 10,000, then a percentile of 50 would mean that there are exactly 5000 people who have a lower rank, and 5000 people who have a higher rank than you.
A 90 percentile implies that 90 percent of people have an overall rank that is lower than yours. And so on.
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2. How are percentiles calculated?
To calculate the kth percentile (where k is any number between zero and one hundred), do the following steps:
A. Order all the values in the data set from smallest to largest.
B. Multiply k percent by the total number of values, n. This number is called the index.
C. If the index obtained in Step 2 is not a whole number, round it up to the nearest whole number and go to Step D.i. If the index obtained in Step 2 is a whole number, go to Step D.ii.
D.i.Count the values in your data set from left to right (from the smallest to the largest value) until you reach the number indicated by Step C. The corresponding value in your data set is the kth percentile.
D.ii.Count the values in your data set from left to right until you reach the number indicated by Step B.
E. The kth percentile is the average of that corresponding value in your data set and the value that directly follows it.
Example:
For example, suppose you have 25 test scores, and in order from lowest to highest they look like this: 43, 54, 56, 61, 62, 66, 68, 69, 69, 70, 71, 72, 77, 78, 79, 85, 87, 88, 89, 93, 95, 96, 98, 99, 99.
To find the 90th percentile for these (ordered) scores, start by multiplying 90% times the total number of scores, which gives 90% ∗ 25 = 0.90 ∗ 25 = 22.5 (the index). Rounding up to the nearest whole number, you get 23.
Counting from left to right (from the smallest to the largest value in the data set), you go until you find the 23rd value in the data set. That value is 98, and it’s the 90th percentile for this data set.
Now say you want to find the 20th percentile. Start by taking 0.20 x 25 = 5 (the index); this is a whole number, so proceed from Step C to Step D.ii, which tells you the 20th percentile is the average of the 5th and 6th values in the ordered data set (62 and 66). The 20th percentile then comes to (62 + 66) ÷ 2 = 64.
The median (the 50th percentile) for the test scores is the 13th score: 77.
The steps shown here demonstrate one way of calculating percentiles, but there are several other acceptable methods. Do not be too alarmed if your calculator or a friend gives you a value close to but different from what these steps would give.
Thus #IRL:
In an exam taken by 10,000 people, if your rank is 80, then your percentile score will be:
[(10000-80)/10000)x100]
or, 9920/100
which gives a percentile score of 99.20.
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3. Why is your percentile isn't anywhere close to the average of the percentile received in all the sections put together.
Simply put, because percentiles are calculated as per:
1. Same method, applied section-wise score.
2. Same method, applied on overall score.
So, if you have received a result as below:
QA - 99.8 - 80
VA - 99.8 - 80
LR/DI - 5 - 0
Then your percentile may be around 95, basis the overall score, but would be comparatively low in the DI/lR section, as noted.
Hope this helps you calculate your own score during mocks.
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References: From
here.
Want to know what percentiles you need to get into the top b-schools of India? Check out this article.
Will I get admission in top B-schools with 98+ percentile?