Find the standard deviation | Statistics | SciPiPupil

Question: Find the standard deviation:

Class Interval	0-10	0-20	0-30	0-40	0-50
Frequency	2	5	10	13	15

Solution:

[Comment: assumed mean is easier way to perform standard deviation, so we use Assumed Mean method]

Taking Assumed Mean (A) = 25

Arranging the given data in a table;

X	f	Mid-value (m)	d(x-25)	d²	fd	fd²
0-10	2	5	-20	400	-40	800
0-20 (10-20)	3	15	-10	100	-30	300
0-30 (20-30)	5	25	0	0	0	0
0-40 (30-40)	3	35	10	100	30	300
0-50 (40-50)	2	45	20	400	40	800
	N = 15				$\sum$fd = 0	$\sum$fd² =2200

Now,

Standard Deviation ($\sigma$) = $\sqrt{ \dfrac{\sum fd²}{N} - \left ( \dfrac{\sum fd}{N} \right )}^2$

$= \sqrt{ \dfrac{2200}{15} - \left ( \dfrac{-0}{15} \right )}^2$

$= \sqrt{ 146.66}$

$= 12.11$

Hence, the required standard deviation of the give data is 12.11.

How to take Assumed Mean?

In this method, the mean is taken as the mid-value of the mid-class from the given data. Here, mid term is mid-class is 20-30 and the mid-value is 25.

Related Notes and Solutions:

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

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