Find the mean deviation about the mean for the data 38, 70, 48, 40, 42, 55, 63, 46, 54, 44

Asked by Pragya Singh | 11 months ago |  83

##### Solution :-

First we have to find (x̅) of the given data

$$\overline{X} = \dfrac{1}{10} \displaystyle\sum_{i=1}^{10} X_i$$

$$\dfrac{500}{10}$$

= 50

So, the respective values of the deviations from mean,

i.e., xi – x̅ are, 50 – 38 = -12, 50 -70 = -20, 50 – 48 = 2, 50 – 40 = 10, 50 – 42 = 8,

50 – 55 = – 5, 50 – 63 = – 13, 50 – 46 = 4, 50 – 54 = -4, 50 – 44 = 6

-12, 20, -2, -10, -8, 5, 13, -4, 4, -6

Now absolute values of the deviations,

12, 20, 2, 10, 8, 5, 13, 4, 4, 6

$$\displaystyle\sum_{i=1}^{10} |X_i-\overline{X}| =84$$

MD = $$\dfrac{sum \;of\; deviations}{number\; of\; observations}$$

$$\dfrac{84}{10}$$

= 8.4

So, the mean deviation for the given data is 8.4.

Answered by Abhisek | 11 months ago

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