Find the standard deviation of the following data: | Standard Deviation | SciPiPupil

Question: Find the standard deviation of the following data:

Class Interval	0-10	10-20	20-30	30-40	40-50
Frequency	5	8	15	16	6

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;

Marks	Frequency (f)	Mid-value (m)	d(x-25)	d²	fd	fd²
0-10	5	5	-20	400	-100	2000
10-20	8	15	-10	100	-80	800
20-30	15	25	0	0	0	0
30-40	16	35	10	100	160	1600
40-50	6	45	20	400	120	2400
	N = 50				$\sum$fd = 100	$\sum$fd² =6800

Now,

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

$= \sqrt{ \dfrac{6800}{50} - \left ( \dfrac{100}{50} \right )}^2$

$= \sqrt{ 136 - (2)²}$

$= \sqrt{136 - 4}$

$= \sqrt{132}$

$= 11.48$

Hence, the required standard deviation of the give data is 11.48.

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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