Measures of dispersion - (16.1-16.3)

Understand the concept of dispersion

  • Theory
  • Examples
  • Solutions

Understand the concepts of range and inter-quartile range

  • Theory
  • Examples
    Find the range and inter-quartile 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) \(\begin{array}{l}Range = 49 - 1\\ = \underline{\underline {48}} \end{array}\)
    \({Q_1} = 4\)
    \({Q_3} = 36\)
    \(\begin{array}{l}Inter-quartile range = 36 - 4\\ = \underline{\underline {32}} \end{array}\)

    (b) Arrange the data in ascending order as follows:
    5, 8, 11, 17, 19, 22, 28, 33
    \(\begin{array}{l} Range= 33 - 5\\ = \underline{\underline {28}} \end{array}\)
    \(\begin{array}{c}{Q_1} = \frac{{8 + 11}}{2}\\ = 9.5\end{array}\)
    \(\begin{array}{c}{Q_3} = \frac{{22 + 28}}{2}\\ = 25\end{array}\)
    \(\begin{array}{l}Inter-quartile range = 25 - 9.5\\ = \underline{\underline {15.5}} \end{array}\)

Construct and interpret the box-and-whisker diagram and use it to compare the distributions of different sets of data

  • Graph
  • Theory
  • Examples
  • Solutions