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

Exercise 13.1 · Q4

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

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Median $= 47.5$ , and the mean deviation about the median is $\dfrac{70}{10} = 7$ .

\text{M.D.}(M) = \frac{\sum |x_i - M|}{n}

1. Arrange the data in ascending order.

36,\ 42,\ 45,\ 46,\ 46,\ 49,\ 51,\ 53,\ 60,\ 72

There are $n = 10$ observations (even).

2. Find the median.

The median is the mean of the $5^{\text{th}}$ and $6^{\text{th}}$ values:

M = \frac{46 + 49}{2} = 47.5

3. 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 for the following data: 36, 72, 46, 42, 60, 45, 53, 46, 51, 49