Find the standard deviation using actual mean. | Standard Deviation | SciPiPupil

Question: Find the standard deviation using actual mean.

X	0-10	10-20	20-30	30-40	40-50	50-60
f	4	6	10	20	6	4

Solution:

Using actual mean,

Arranging the data in a table,

X	f	m	fm	d|x-31|	d²	fd²
0-10	4	5	20	26	676	2704
10-20	6	15	90	16	256	1536
20-30	10	25	250	-6	36	360
30-40	20	35	700	4	16	320
40-50	6	45	270	14	196	1176
50-60	4	55	220	24	576	2304
	N=50		$\sum$fm  = 1550			$\sum$fd²=8400

Now,

Mean = $\dfrac{\sum fm}{N}$

$= \dfrac{1550}{50}$

$= 31$
 

Standard Deviation ($\sigma$) = $ \sqrt{ \dfrac{\sum fd²}{N} }$

$= \sqrt{ \dfrac{8400}{50} }$

$= \sqrt{168}$

$= 12.96$

Hence, the required standard deviation using actual mean of the given data is 12.96.

Related Notes and Solutions:

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

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