Find the standard deviation and its coefficient from the given 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 15 25 35 45

Solution:

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 15 15 -10 100 -150 1500
20-30 25 25 0 0 0 0
30-40 35 35 10 100 350 3500
40-50 45 45 20 400 900 18000
N = 125 $\sum$fd
= 1000 $\sum$fd²
=25000

The mean of the given data is

m f fm

5 5 25

15 15 225

25 25 625

35 35 1225

45 45 2025

N=125 $\sum$fm = 4125

Mean = $\dfrac{ \sum fm}{N}$
$= \dfrac{4125}{125}$
$= 33$

Now,

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

$= \sqrt{ \dfrac{25000}{125} - \left ( \dfrac{1000}{125} \right )}^2$

$= \sqrt{ 200 - (8)²}$

$= \sqrt{200 - 64}$

$= \sqrt{136}$

$= 11.66$

And,

Coefficient of Standard Deviation = $\dfrac{\sigma}{mean}$

$= \dfrac{11.66}{33}$

$= 0.35$

Hence, the required standard deviation of the give data is 11.48 and the coefficient of standard deviation is 0.35.

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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