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

Question: Find the standard deviation of the following data:

Class Interval	25-35	35-45	45-55	55-65	65-75
Frequency	5	4	6	7	3

Solution:

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

Taking Assumed Mean (A) = 50

Arranging the given data in a table;

Marks	Frequency (f)	Mid-value (m)	d(x-50)	d²	fd	fd²
25-35	5	30	-20	400	-100	2000
35-45	4	40	-10	100	-40	400
45-55	6	50	0	0	0	0
55-65	7	60	10	100	70	700
65-75	3	70	20	400	60	1200
	N = 25				$\sum$fd = -10	$\sum$fd² =4300

Now,

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

$= \sqrt{ \dfrac{4300}{25} - \left ( \dfrac{-10}{25} \right )}^2$

$= \sqrt{ 172 - (-0.4)²}$

$= \sqrt{172- 0.16}$

$= \sqrt{171.84}$

$= 13.108$

$= 13.11$

Hence, the required standard deviation of the give data is 13.08.

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 45-55 and the mid-value is 50.

Related Notes and Solutions:

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

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