What is Range, quartiles? — Mathematics

Definition 8.7 High School Mathematics · Chapter 8 — Descriptive Statistics

For a sorted series:

the range is the difference between the largest and smallest values;
the first quartile $Q_1$ is the smallest value such that at least a quarter ( $25\%$ ) of the values are $\leq Q_1$ ; the third quartile $Q_3$ is the smallest value such that at least three quarters ( $75\%$ ) of the values are $\leq Q_3$ ;
the interquartile range $Q_3 - Q_1$ measures the spread of the central half of the data.

The box plot of : the box spans the interquartile interval [Q_1, Q_3] and contains the central half of the data; the whiskers reach the extreme values. — The box plot of Example 8.9: the box spans the interquartile interval $\intcc{Q_1}{Q_3}$ and contains the central half of the data; the whiskers reach the extreme values.

Examples

Example 8.9

Take the $11$ sorted values

2,\ 3,\ 5,\ 5,\ 6,\ 7,\ 8,\ 9,\ 9,\ 10,\ 12 .

Median: position $\frac{11+1}{2} = 6$ , so the median is $7$ . $Q_1$ : $\frac{11}{4} = 2.75$ , round up to $3$ ; the $3$ rd value is $5$ . $Q_3$ : $\frac{33}{4} = 8.25$ , round up to $9$ ; the $9$ th value is $9$ . Range: $12 - 2 = 10$ ; interquartile range: $9 - 5 = 4$ .

Read in context →