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The mean deviation about the mean for the following data, is
\begin{array}{c|c|c|c|c|c}
\hline \boldsymbol{x}_i & 2 & 4 & 5 & 7 & 9 \\
\hline \boldsymbol{f}_i & 2 & 4 & 10 & 8 & 6 \\
\hline
\end{array}
Options:
\begin{array}{c|c|c|c|c|c}
\hline \boldsymbol{x}_i & 2 & 4 & 5 & 7 & 9 \\
\hline \boldsymbol{f}_i & 2 & 4 & 10 & 8 & 6 \\
\hline
\end{array}
Solution:
2238 Upvotes
Verified Answer
The correct answer is:
1.733
We have, the following data.
Here, mean
$$
\text { (र) }=\frac{\sum x_1 f_i}{\sum f_i}=\frac{4+16+50+56+54}{2+4+10+8+6}=\frac{180}{30}=6
$$
$\therefore$ Mean deviation about mean $=\frac{\sum f_i\left|x_{\dot{i}}-\bar{x}\right|}{\sum f_{\dot{i}}}$
$$
\begin{aligned}
& =\frac{2 \cdot(4)+4 \cdot(2)+10 \cdot(1)+8 \cdot(1)+6 \cdot(3)}{30} \\
& =\frac{8+8+10+8+18}{30}=\frac{52}{30} \approx \frac{17.33}{10}=1.733
\end{aligned}
$$
Here, mean
$$
\text { (र) }=\frac{\sum x_1 f_i}{\sum f_i}=\frac{4+16+50+56+54}{2+4+10+8+6}=\frac{180}{30}=6
$$
$\therefore$ Mean deviation about mean $=\frac{\sum f_i\left|x_{\dot{i}}-\bar{x}\right|}{\sum f_{\dot{i}}}$
$$
\begin{aligned}
& =\frac{2 \cdot(4)+4 \cdot(2)+10 \cdot(1)+8 \cdot(1)+6 \cdot(3)}{30} \\
& =\frac{8+8+10+8+18}{30}=\frac{52}{30} \approx \frac{17.33}{10}=1.733
\end{aligned}
$$
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