From the follwing data, find the standard deviation and coefficient of variation. | Statistics | SciPiPupil

Question: From the following data, find the standard deviation and coefficient of variation.

Class Interval	20-30	30-40	40-50	50-60	60-70	70-80
Frequency	10	15	25	30	12	8

Solution:

Using actual mean,

[We have, interval between two classes is 10.

To get the frequency, subtract the give frequency of the respective class from one step higher class.]

Arranging the data in a table,

X	f	m	fm	d|x-21.5|	d²	fd²
20-30	10	25	250	24.3	590.49	5904.9
30-40	15	35	525	14.3	204.49	3067.35
40-50	25	45	1125	4.3	18.49	462.25
30-40	30	55	1650	5.7	32.49	974.7
40-50	12	65	780	15.7	246.49	2957.88
70-80	8	75	600	25.7	660.49	5283.92
	N=100		$\sum$fm  = 4930			$\sum$fd² =18651

Now,

Mean = $\dfrac{\sum fm}{N}$

$= \dfrac{4930}{100}$

$= 49.3$
 

Standard Deviation ($\sigma$) = $\sqrt{ \dfrac{\sum fd²}{N} }$

$= \sqrt{ \dfrac{18651}{100} }$

$= \sqrt{186.51}$

$= 13.66$

And,

Coefficient of Variation = $\dfrac{\sigma}{mean} × 100%$

$= \dfrac{13.66}{49.3} × 100%$

$= 0.2770 × 100%$

$= 27.7%$

Hence, the required standard deviation using actual mean of the given data is 13.66 and the coefficient of variation is 27.7%.

Related Notes and Solutions:

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

#SciPiPupil