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 :
Solution
<p>$$\begin{aligned}
&\begin{aligned}
& \frac{2+3+3+4+5+7+a+b}{8}=4 \\
& \Rightarrow a+b=8 \\
& (\sqrt{2})^2=\frac{2^2+3^2+3^2+4^2+5^2+7^2+a^2+b^2}{8}-16 \\
& 112+a^2+b^2=18 \times 8 \\
& \Rightarrow a^2+b^2=32 \\
& \Rightarrow a=b=4
\end{aligned}\\
&\text { Now numbers be }\\
&2,3,3,4,4,4,5,7
\end{aligned}$$</p>
<p>Mode $=4$</p>
<p>Mean deviation about mode :</p>
<p>$$\begin{aligned}
& \frac{|2-4|+|3-4|+|3-4|+0+0+0+|5-4|+|4-7|}{8} \\
= & \frac{2+1+1+1+3}{8}=\frac{8}{8}=1
\end{aligned}$$</p>
About this question
Subject: Mathematics · Chapter: Statistics · Topic: Measures of Central Tendency
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