Calculate the mean deviation about median age for the age distribution of \[100\] persons given below: [Hint Convert the given data into continuous frequency distribution by subtracting \[0.5\] from the lower limit and adding \[0.5\] to the upper limit of each class interval] - Noon Academy

Calculate the mean deviation about median age for the age distribution of

$100$

persons given below: [Hint Convert the given data into continuous frequency distribution by subtracting

$0.5$

from the lower limit and adding

$0.5$

to the upper limit of each class interval]

Class 11 | Exercise 15.1 | Maths | NCERT | Statistics

Calculate the mean deviation about median age for the age distribution of

$100$

persons given below: [Hint Convert the given data into continuous frequency distribution by subtracting

$0.5$

from the lower limit and adding

$0.5$

to the upper limit of each class interval]

Solution:-

The given data is converted into continuous frequency distribution by subtracting

$0.5$

from the lower limit and adding the

$0.5$

to the upper limit of each class intervals and append other columns after calculations.

The class interval containing

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

or

$50$

item is

$35.5-40.5$

So,

$35.5-40.5$

is the median class.

Then,

Median = l + (((N/

$2$

) – c)/f) × h

Where, l =

$35.5$

, c =

$37$

, f =

$26$

, h =

$5$

and n =

$100$

Median =

$35.5+(((50-37))/26)\times 5$

=

$35.5+2.5$

=

$38$

So

$\sum\limits_{i=1}^{6}{{{f}_{i}}\left| {{x}_{i}}-Med \right|=735}$

And M.D.(M) =

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

=

$(1/100)\times 735$

=

$7.35$

Therefore, the mean deviationabout the median is

$7.35$

i

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