From the following 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	0-10	0-20	0-30	0-40	0-50
Frequency	8	18	30	38	40

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
0-10	8	5	40	16.5	272.25	2178
0-20 (10-20)	10	15	150	6.5	42.25	422.5
0-30 (20-30)	12	25	300	3.5	12.25	147
0-40 (30-40)	8	35	280	13.5	182.25	1458
0-50 (40-50)	2	45	90	23.5	552.25	1104.5
	N=40		$\sum$fm  = 860			$\sum$fd² =5310

Now,

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

$= \dfrac{860}{40}$

$= 21.5$
 

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

$= \sqrt{ \dfrac{5310}{40} }$

$= \sqrt{132.75}$

$= 11.52$

And,

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

$= \dfrac{11.52}{21.5} × 100%$

$= 0.5358 × 100%$

$= 53.58%$

Hence, the required standard deviation using actual mean of the given data is 11.52 and the coefficient of variation is 53.58%.

Related Notes and Solutions:

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

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