To find the percentile of a given value in a data set, follow these steps:
- Arrange the data values in ascending order.
- Count how many values in the data set are below the given value.
- Use the formula:
Percentile=(Number of values below the given valueTotal number of values in the data set)×100\text{Percentile}=\left(\frac{\text{Number of values below the given value}}{\text{Total number of values in the data set}}\right)\times 100Percentile=(Total number of values in the data setNumber of values below the given value)×100
This gives the percentile as the percentage of values below the given number. For example, if 10 values are below your value out of 15 total values, your percentile is 1015×100=66.7%\frac{10}{15}\times 100=66.7%1510×100=66.7%.
For a given percentile ppp, you can also find the rank rrr in the data using the formula:
r=p100×(n−1)+1r=\frac{p}{100}\times (n-1)+1r=100p×(n−1)+1
where nnn is the number of data points. You then find the value at rank rrr or interpolate if rrr is not an integer to get the value at that percentile.
This method is used in statistics to understand how a value compares to the rest of the data set.
