# Mean Deviation

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• Q1

Compute the mean deviation about the median for the following frequency distribution.

 Variable(x) 8 10 15 20 25 32 35 Frequency(f) 3 2 4 7 4 3 7

Marks:3

We construct the following table. Firstly, we compute the median.

 x f (c.f.) xi - Median |xi - Median| f|xi - Median| 8 3 3 -12 12 36 10 2 5 -10 10 20 15 4 9 -5 5 20 20 7 16 0 0 0 25 4 20 5 5 20 32 3 23 12 12 36 35 7 30 15 15 105 f=N= 30 f|xi - Median| = 237

Here N = 30, which is even.
The median will be an average of the (N/2)th and (N+1)/2 th observations. i.e., 15th and 16th observations.
So, Median = (20+20)/ 2 = 20.

• Q2

Find the mean deviation about the median for the following data:

 Class 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 7 15 6 16 2 4

Marks:5

We construct the following table:

The class-interval containing (N/2)th or 25th item is 20-30. Therefore, it is the median class.

Here, l = 20, N = 50, C = 22, f= 6 and h = 10

= 20+{(50/2 - 22)}/6 10=25

M.D.( ) = = 610/50= 12.2

• Q3

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

 Class Interval 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Frequency 2 3 8 14 8 3 2

Marks:5

We construct the following table:

 Class Interval f Midpoint of class, x fx = x – 45 f 10-20 2 15 30 -30 30 60 20-30 3 25 75 -20 20 60 30-40 8 35 280 -10 10 80 40-50 14 45 630 0 0 0 50-60 8 55 440 10 10 80 60-70 3 65 195 20 20 60 70-80 2 75 150 30 30 60 N = 40 fx=1800 =400

= (fx) / N = 1800/40 = 45

M.D.() =( )/N = 400/40=10

• Q4

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

 x 3 5 7 9 11 13 f 2 7 10 9 5 2

Marks:3

We construct the following table:

 x f fx = x – 7.8 f 3 2 6 - 4.8 4.8 9.6 5 7 35 - 2.8 2.8 19.6 7 10 70 - 0.8 0.8 8.0 9 9 81 1.2 1.2 10.8 11 5 55 3.2 3.2 16.0 13 2 26 5.2 5.2 10.4 N = 35 fx=273 = 74.4