Question

Calculate the mean, median and mode for the following data: 23, 17, 14, 17, 21, 14,

23, 21, 16, 14, 16, 18, 20, 22, 25, 24, 17, 29, 10.

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{given}\mathrm{data}\mathrm{in}\mathrm{ascending}\mathrm{order}\mathrm{is}, \\ 10,14,14,14,16,16,17,17,17,18,20,21,21,22,23,23,24,25,29. \\ \mathrm{Sum}\mathrm{of}\mathrm{observations}=10+14+14+14+16+16+17+17+17+18+20+21+21+22+23+23+24+25+29=361 \\ \mathrm{Number}\mathrm{of}\mathrm{observations}=19 \\ \mathrm{Mean}=\frac{\mathrm{sum}\mathrm{of}\mathrm{observations}}{\mathrm{number}\mathrm{of}\mathrm{observations}}=\frac{361}{19}=19 \\ \mathrm{Now},\mathrm{number}\mathrm{of}\mathrm{observations}\left(\mathrm{n}\right)=19\left(\mathrm{odd}\right) \\ \mathrm{median}=\mathrm{value}\mathrm{of}{\left(\frac{\mathrm{n}+1}{2}\right)}^{\mathrm{th}}\mathrm{observation}=\mathrm{value}\mathrm{of}{\left(\frac{19+1}{2}\right)}^{\mathrm{th}}\mathrm{observation} \\ =\mathrm{value}\mathrm{of}{10}^{\mathrm{th}}\mathrm{observation}=18 \\ \mathrm{Since}\mathrm{the}\mathrm{observation}14\mathrm{and}17\mathrm{appears}\mathrm{more}\mathrm{frequently}\mathrm{in}\mathrm{the}\mathrm{data},\mathrm{so}\mathrm{the}\mathrm{mode}\mathrm{of}\mathrm{the}\mathrm{data}\mathrm{is}14\mathrm{and}17. \end{gathered}$$