Measures of dispersion  (16.116.3)
Understand the concept of dispersion

Theory

Examples

Solutions
Understand the concepts of range and interquartile range

Theory

ExamplesFind the range and interquartile range for each of the following sets of data.
(a) 1, 4, 9, 16, 25, 36, 49
(b) 22, 5, 17, 28, 33, 8, 19, 11

Solutions(a) \(\begin{array}{l}Range = 49  1\\ = \underline{\underline {48}} \end{array}\)
\({Q_1} = 4\)
\({Q_3} = 36\)
\(\begin{array}{l}Interquartile range = 36  4\\ = \underline{\underline {32}} \end{array}\)
(b) Arrange the data in ascending order as follows:
5, 8, 11, 17, 19, 22, 28, 33
\(\begin{array}{l} Range= 33  5\\ = \underline{\underline {28}} \end{array}\)
\(\begin{array}{c}{Q_1} = \frac{{8 + 11}}{2}\\ = 9.5\end{array}\)
\(\begin{array}{c}{Q_3} = \frac{{22 + 28}}{2}\\ = 25\end{array}\)
\(\begin{array}{l}Interquartile range = 25  9.5\\ = \underline{\underline {15.5}} \end{array}\)
Construct and interpret the boxandwhisker diagram and use it to compare the distributions of different sets of data

Graph

Theory

Examples

Solutions