Quartile

Quartiles are special percentiles: the 1st quartile, $Q_{1}$ , is equal to the 25th percentile; the 3rd quartile, $q_{3}$ , is equal to the 75th percentile. The Median is both the 2nd quartile ( $Q_{2}$ ) and the 50th Percentile.

To calculate quartiles, the data must be ordered from smallest to largest.

quartile

Quartiles divide ordered data into quarters.

There are 4 quartiles:

[[#1st Quartile]]
[[#2nd Quartile]]
[[#3rd Quartile]]
[[#4th Quartile]]

A useful value is the Interquartile Range (IQR).

1st Quartile

2nd Quartile

The 2nd quartile is also known as Median:

Median

Median is a number that measures the center of the data. It can be thought of as the middle value, but is not necessarily one of the observed values.

It separates ordered data into halves.

median

The Median is the value of a sample $X$ such that the probability of getting a value less than the median is equal to the prbability of getting a value greater than the median and is equal to 0.5.

50% of the observations are less than the median
50% of the observations are more than the median