In statistics, any one of the three values that divide data into four equal parts. They comprise the lower quartile, below which lies the lowest 25% of the data; the median, which is the middle 50%, half way through the data; and the upper quartile, above which lies the top 25%. The difference of value between the upper and lower quartiles is known as the interquartile range, which is a useful measure of the dispersion of a statistical distribution because it is not affected by freak extreme values (see range). These values are usually found using a cumulative frequency diagram.
For example, a football team scored the following goals in one season:
This information can be displayed in a cumulative frequency curve:
From the curve, the median is 2.4 goals, the lower quartile is 1.2 goals, and the upper quartile is 3.4 goals. The interquartile range is 3.4 − 1.2, which is 2.2 goals.
The lower quartile may also be described as the 25th percentile; the median as the 50th percentile; and the upper quartile as the 75th percentile.
Cumulative frequencies and medians
Box and Whiskers Plots
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