Find the mean deviation about the median for the data. 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

Asked by Pragya Singh | 1 year ago |  90

##### Solution :-

First we have to arrange the given observations into ascending order,

10, 11, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18.

The number of observations is 12

Then,

Median = $$\dfrac{(\dfrac{12}{2})^{th}observation+(\dfrac{12+1}{2})^{th}}{2}$$

($$\dfrac{12}{2}$$)th observation = 6th = 13

($$\dfrac{12}{2}$$)+ 1)th observation = 6 + 1

= 7th = 14

Median = $$\dfrac{(13 + 14)}{2}$$

=$$\dfrac{27}{2}$$

= 13.5

So, the absolute values of the respective deviations from the median, i.e., |xi – M| are

3.5, 2.5, 2.5, 1.5, 0.5, 0.5, 0.5, 2.5, 2.5, 3.5, 3.5, 4.5

$$\displaystyle\sum_{i=1}^{12} |X_i-M|=28$$

Mean Deviation,

$$MD(M) = \dfrac{1}{12} \displaystyle\sum_{i=1}^{12} |x_i-M|$$

$$\dfrac{1}{12} \times 28$$

= 2.33

So, the mean deviation about the median for the given data is 2.33.

Answered by Pragya Singh | 1 year ago

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