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

Related Questions

Find the mean deviation from the mean and from a median of the following distribution

Find the mean deviation from the mean and from a median of the following distribution:

 Marks 0-10 10-20 20-30 30-40 40-50 No. of students 5 8 15 16 6

The age distribution of 100 life-insurance policy holders is as follows:

The age distribution of 100 life-insurance policy holders is as follows

 Age (on nearest birthday) 17-19.5 20-25.5 26-35.5 36-40.5 41-50.5 51-55.5 56-60.5 61-70.5 No. of persons 5 16 12 26 14 12 6 5

Compute mean deviation from mean of the following distribution:

Compute mean deviation from mean of the following distribution:

 Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 No. of students 8 10 15 25 20 18 9 5

Find the mean deviation from the mean for the following data

Find the mean deviation from the mean for the following data:

 Classes 95-105 105-115 115-125 125-135 135-145 145-155 Frequencies 9 13 16 26 30 12