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The mean deviation about the mean for the following data:
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Verified Answer
The correct answer is:
$23.84$
Mean $(\bar{x})=\frac{\Sigma f_i x_i}{\Sigma f_i}=\frac{2560}{50}=51.2$
Mean deviation about mean $=\frac{\Sigma f_i\left|x_i-\bar{x}\right|}{\Sigma f_i}$
$\begin{aligned} & \frac{1}{50}\left\{\begin{array}{l}10 \mid(10-51.2|+8| 30-51.2|+12| 50-51.2 \mid \\ +9|70-51.2|+11|90-51.2|\end{array}\right\} \\ & \frac{1}{50}[412+169.6+14.4+169.2+426.8] \\ & =23.84\end{aligned}$
Mean deviation about mean $=\frac{\Sigma f_i\left|x_i-\bar{x}\right|}{\Sigma f_i}$
$\begin{aligned} & \frac{1}{50}\left\{\begin{array}{l}10 \mid(10-51.2|+8| 30-51.2|+12| 50-51.2 \mid \\ +9|70-51.2|+11|90-51.2|\end{array}\right\} \\ & \frac{1}{50}[412+169.6+14.4+169.2+426.8] \\ & =23.84\end{aligned}$
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