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The mean deviation about the median of the discrete data $12,15,7,4,4,15,23,14$ is
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Verified Answer
The correct answer is:
5
Given data in ascending order is $4,4,7,12$, $14,15,15,23$
Here, number of terms, $n=8$, which is even.
So, median
$$
\begin{aligned}
& =\frac{\left(\frac{n}{2}\right) \text { th term }+\left(\frac{n}{1}+1\right) \text { th term }}{2} \\
& =\frac{4 \text { th term }+5 \text { th term }}{2}=\frac{12+14}{2}=13
\end{aligned}
$$
Calculation of mean deviation about median
Hence, mean deviation about median
$$
=\frac{\sum\left|d_i\right|}{n}=\frac{40}{8}=5
$$
Here, number of terms, $n=8$, which is even.
So, median
$$
\begin{aligned}
& =\frac{\left(\frac{n}{2}\right) \text { th term }+\left(\frac{n}{1}+1\right) \text { th term }}{2} \\
& =\frac{4 \text { th term }+5 \text { th term }}{2}=\frac{12+14}{2}=13
\end{aligned}
$$
Calculation of mean deviation about median
Hence, mean deviation about median
$$
=\frac{\sum\left|d_i\right|}{n}=\frac{40}{8}=5
$$
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