Percentiles

Percentiles

A percentile gives you a sense where a given number is ranked, relative to other numbers, within a dataset.

Example

If your midterm grade is in the top 10% percentile in your class, that means your midterm grade is in the top 10% when being compared to all other students' midterm grades in your class.

Steps for Determining Percentiles

1. Arrange your data set (sample) from lowest to highest numbers.
2. Compute $\displaystyle \boxed{i=\frac{p}{100} n}$ where
3. $p$ is the desired %
4. $n$ is sample size, and
5. $i$ is the location of the percentile
6. Look at $i$.
7. If $i$ is not a whole number, then you round up to the $(i+1)^{th}$ number to get your desired percentile.
8. If $i$ is a whole number, the desired percentile is the average of $i$th and $(i+1)$th numbers.

Quartiles

• To solve for the first quartile, Q1, $p=0.25$
• To solve for the median, Q2, $p=0.50$
• To solve for the third quartile, Q3, $p=0.75$