Find the mean deviation and its coefficient about from the following data: | Statistics | SciPiPupil

Question: Find the mean deviation and its coefficient about from the following data:

Mark	0-10	0-20	0-30	0-40	0-50
Frequency	5	13	28	44	50

Solution:

Arranging data in a table,

Marks	Frequency (f)	Mid Value(x)	fx	|x-x̄|	f|x-x̄|
0-10	5	5	25	22	110
0-20 (10-20)	8	15	120	12	96
0-30 (20-30)	15	25	375	2	30
(0-40) 30-40	16	35	560	8	128
(0-50) 40-50	6	45	270	18	108
	N= 50		$\sum$fx = 1350		$\sum$f|x-x̄| = 472

Now,

Mean (x̄) =$\dfrac{\sum fx}{N}$

$= \dfrac{1350}{50}$

$= 27$

And,

Mean Deviation from Mean (M.D.) = $\dfrac{\sum f|x-x̄|}{N}$

$= \dfrac{472}{50}$

$= 9.44$

Also,

Coefficient of M.D. = $\dfrac{M.D.}{x̄}$

$= \dfrac{9.44}{27}$

$= 0.349$

$= 0.35$

Hence, the required mean deviation about the mean of the given data is 9.44 and coefficient of mean deviation is 0.35.

Related Notes and Solutions:

Here is the website link to the notes of Statistics of Class 10.

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