Find standard deviation

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written 2.0 years ago by

Solution:

Class	$f_i$	$x_i$	$u_i$	$ui^2$	$fiui$	$fiui^2$
0-10	3	5	-2	4	-6	12
10-20	5	15	-1	1	5	5
20-30	8	25=A	0	0	0	0
30-40	3	35	1	1	3	3
40-50	1	45	2	4	4	4
	$\sum \mathrm{f}{\mathrm{i}}=$20				$\sum \mathrm{u}{\mathrm{i}} \mathrm{f}{\mathrm{i}}$= 6	$\sum \mathrm{u}{\mathrm{i}}^{2} \mathrm{f}{\mathrm{i}}$= 24

Mean:

$\overline{\mathrm{X}}=\mathrm{A}+\mathrm{h}\left(\frac{\sum \mathrm{u}{\mathrm{i}} \mathrm{f}{\mathrm{i}}}{\mathrm{N}}\right)$

$ =25+10\left(\frac{6}{20}\right)$

= 28

Variance:

$ \operatorname{Var}(X)=h^{2}\left[\frac{1}{N} \sum_{i=1}^{n} f_{i} u_{i}^{2}-\left(\frac{1}{N} \sum_{i=1}^{n} u_{i} f_{i}\right)^{2}\right] $

$ =100\left[\frac{24}{20}-\frac{36}{400}\right] $

$ =100[1.2 - 0.09] $

$ =111 $

Standard Deviation:

$\sigma=\sqrt{111}$

= 10.53

The standard deviation is $10.53$

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