Question

Calculate mean deviation and it's coefficient of mean deviation about median from the following Data. Size below 10 20 30 40 50 frequency 1and 3 7 8 10

Answer 1

The mean deviation about median is 8.9655and its coefficient is 0.598.

Given:

Size (x)             10.      20      30       40       50

Frequency (f)    1          3         7        8         10

To find:

Mean deviation and its coefficient about median

Solution:

First compute the cumulative frequency (cf) of the data

Size (x)             10       20      30       40       50

Frequency (f)    1          3         7        8         10

cf                       1          4         11        19        29

|x-M|                  30       20      10        0         10

f|x-M|                 30       60       70      0        100

Total number of frequencies (N) = 29

To find median we will use the formula,

Median (M) = Size of $\frac{N+1}{2}^{th$term

=$\frac{29+1}{2}^{th}$ term

=$\frac{30}{2}$

=15th term

The 15th term falls under size 40.

Our median is x=40.

∑f|x-M| = 260

The formula for mean deviation MD (M) about median is ∑$\frac{f|x-M|}{N}$

Substitute the values int he formula,

MD of M= 260/29

=8.9655

Coefficient of MD (M) = MD/M

=8.9655/15

=0.598

Therefore, mean deviation and its coefficient about median are 8.9655 and 0.598.

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