Finding the median quartiles and percentiles

Introduction to Median, Quartiles and Percentiles

The median is a measure of central tendency that separates the data into two equal halves. It is the value that sits in the middle of the ordered data set when arranged in ascending or descending order.
Quartiles are values that divide a data series into four equal parts. There are three quartiles: the lower quartile (Q1), the median (Q2), and the upper quartile (Q3).
Percentiles are measures that denote the value below which a given percentage (or proportion) of observed data falls.

To find the median, order your observations from least to greatest. If the number of observations is odd, the median is the middle value. If the number of observations is even, the median is the average of the two middle values.

To find the lower quartile (Q1), select the median of the lower half of your data (not including the median in case of odd-sized data).
The upper quartile (Q3) is calculated similarly, by finding the median of the upper half of the data.
The difference between Q3 and Q1 is referred to as the interquartile range (IQR) and it describes the spread of the central 50% of values.

Percentiles are calculated similarly to the median and quartiles. To find the pth percentile (where p is any number from 0 to 100), arrange your data in order and then find the number that aligns at the pth percentage.
For example, the 20th percentile is the value below which 20% of the observations may be found.

The median, quartiles, and percentiles are all measures of position in a dataset, giving a sense of where a particular value stands relative to the rest of the data.
The position and spread of these measures give an idea about the distribution of the data: its central tendency, spread, and skewness. They are particularly useful in skewed distributions where the mean might not be a useful measure.

Note: Understanding these concepts and how to calculate them gives you powerful tools for describing and understanding data.