A percentile is a type of quartile which divides the given probability distribution, or sample, into 100 equal-sized intervals; this allows the data to be analyzed in terms of percentages.
Percentiles are useful anytime that a set of data needs to be broken into digestible chunks.
Formula to calculate percentile.
- Arrange the values in the data set in order from smallest to largest.
- Multiply k (percent) by n (total number of values in the data set). This is the index.
- If the index is not a round number, round it up to the nearest whole number.
- Use your ranked data set to find your percentile by counting the values in your data set from smallest to largest until you reach the number ranked that you are looking for.
Example:
Find the 50th percentile of the data below.
3, 6, 7, 8, 9, 2, 6
- We begin by arranging them from smallest to largest.
2, 3, 6, 6, 7, 8, 9
- Then multiply 0.5 (50%) by 7, since we have 7 values.
= 0.5 x 7
= 3.5
- If we round up 3.5, we get 4. So we look for the fourth value in our data set.
2, 3, 6, 6, 7, 8, 9
Since the value for the 50th percentile must be greater than the first four values, the 5th ranked value would be the kth (50th) percentile. In this data set, that value is 7.
We get the 50th percentile by finding the average of 6 and 7.
= 6 + 7
= 13 รท 2
= 6.5
Therefore, your 50th percentile is 6.5.
