Find the mean deviation about the median for the data.

 xi 5 7 9 10 12 15 fi 8 6 2 2 2 6

Asked by Pragya Singh | 1 year ago |  90

##### Solution :-

Let us make the table of the given data and append other columns after calculations.

Now, N = 26, which is even.

Median is the mean of the 13th and 14th observations. Both of these observations lie in the cumulative frequency 14, for which the corresponding observation is 7.

Then,

Median = $$\dfrac{ (13^{th} observation + 14^{th} observation)}{2}$$

$$\dfrac{ (7 + 7)}{2}$$

$$\dfrac{14}{2}$$

= 7

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

Therefore,

$$\displaystyle\sum_{i=1}^{6} f_i =26$$ and $$\displaystyle\sum_{i=1}^{8} f_i|X_i-M|=84$$

$$\overline{X} = \dfrac{1}{N} \displaystyle\sum_{i=1}^{6} f_i |X_i-M|$$

$$\dfrac{1}{26}\times 84$$

= 3.23

Answered by Abhisek | 1 year ago

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