Find the mean deviation about median for the following data: - Noon Academy

Find the mean deviation about median for the following data:

Class 11 | Exercise 15.1 | Maths | NCERT | Statistics

Find the mean deviation about median for the following data:

Solution:-

Draw the table of the given data and append other columns after calculations.

The class interval containing

${{N}^{th}}/2$

or

$25$

item is

$20-30$

So,

$20-30$

is the median class.

Then,

Median = l + (((N/

$2$

) – c)/f) × h

Where, l =

$20$

, c =

$14$

, f =

$14$

, h =

$10$

and n =

$50$

Median =

$20+(((25-14))/14)\times 10$

=

$20+7.85$

=

$27.85$

So

$\sum\limits_{i=1}^{6}{{{f}_{i}}\left| {{x}_{i}}-Med \right|=517.1}$

And M.D.(M) =

$\frac{1}{N}\sum\limits_{i=1}^{6}{{{f}_{i}}\left| {{x}_{i}}-Med \right|}$

=

$(1/50)\times 517.1$

=

$10.34$

Therefore, the mean deviationabout the median is

$10.34$

i

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