Let the mean and the standard deviation of the observation 2,3,3,4,5,7, a, b be 4 and √2 r…

Question

Let the mean and the standard deviation of the observation $2,3,3,4,5,7, a, b$ be 4 and $\sqrt{2}$ respectively. Then the mean deviation about the mode of these observations is :

Accepted Answer

$\begin{gathered} \frac{2+3+3+4+5+7+a+b}{8}=4 \ \Rightarrow a+b=8 \ (\sqrt{2}{)}^{2}=\frac{{2}^{2}+{3}^{2}+{3}^{2}+{4}^{2}+{5}^{2}+{7}^{2}+{a}^{2}+{b}^{2}}{8}-16 \ 112+{a}^{2}+{b}^{2}=18	imes 8 \ \Rightarrow {a}^{2}+{b}^{2}=32 \ \Rightarrow a=b=4 \ \ 2,3,3,4,4,4,5,7 $

Mode $=4$

Mean deviation about mode :

$ \frac{|2-4|+|3-4|+|3-4|+0+0+0+|5-4|+|4-7|}{8} \ = \frac{2+1+1+1+3}{8}=\frac{8}{8}=1 \end{gathered}$

Solutions · 1