Find the mean deviation about the median of the data : 36, 72, 46, 42, 60, 45, 53, 46, 51, 49.

Question

Accepted Answer

>

> [!TLDR]
> Median $=47.5$; averaging $|x_i-47.5|$ over all 10 values gives mean deviation $=7$.
>
> Arrange the data in ascending order:
> $$36,\ 42,\ 45,\ 46,\ 46,\ 49,\ 51,\ 53,\ 60,\ 72.$$
>
> With $n=10$ (even), the median is the average of the 5th and 6th values:
> $$	ext{Median} = \dfrac{46+49}{2} = 47.5.$$
>
> Compute absolute deviations $|x_i - 47.5|$:
>
> | $x_i$ | 36 | 42 | 45 | 46 | 46 | 49 | 51 | 53 | 60 | 72 |
> |---|---|---|---|---|---|---|---|---|---|---| …

Q.Find the mean deviation about the median of the data : 36, 72, 46, 42, 60, 45, 53, 46, 51, 49.

Concept understanding — Mean Deviation about the Mean and Median

Q.Find the mean deviation about the median of the data : 36, 72, 46, 42, 60, 45, 53, 46, 51, 49.

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