Find the standard deviation using assumed mean. | Statistics | SciPiPupil

Question: Find the standard deviation of the following data:

Wage (in RS.)	60-62	63-65	66-68	69-71	72-74
No. Of Workers	5	18	42	27	8

Solution:

Using assumed mean method [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 66-68 and the mid-value is 67]

Taking Assumed Mean (A) = 67

Arranging the given data in a table;

Marks	Frequency (f)	Mid-value (m)	d(x-50)	d²	fd	fd²
60-62	5	61	-6	36	-30	180
63-65	18	64	-3	9	-54	162
66-68	42	67	0	0	0	0
69-71	27	70	3	9	81	243
72-74	8	73	6	36	45	288
	N =100				$\sum$fd = -45	$\sum$fd² =883

Now,

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

$= \sqrt{ \dfrac{873}{100} - \left ( \dfrac{-45}{100} \right )}^2$

$= \sqrt{ 8.73 - (-0.45)²}$

$= \sqrt{8.73- 0.2025}$

$= \sqrt{8.5275}$

$= 2.92$

$= 13.11$

Hence, the required standard deviation of the give data using assumed mean is 2.92.

Related Notes and Solutions:

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

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