Find mean, standard deviation an coefficient of variance of the following data

C.I	0-10	10-20	20-30	30-40	40-50
frequency	3	5	8	3	1

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written 5.2 years ago by

teamques10 ★ 68k

• modified 5.2 years ago

Solution:

class	$x_{i}$	$f_{i}$	$f_{i}x_{i}$	$d_{i}=\frac{x_{i}-a}{h}$	$f_{i}d_{i}$	$d_{i}^{2}$	$f_{i}d_{i}^{2}$
0-10	5	3	15	-2	-6	4	12
10-20	15	5	75	-1	-5	1	5
20-30	25	8	200	0	0	0	0
30-40	35	3	105	1	3	1	3
40-50	45	1	45	2	2	4	4
		20	440		-6		24

$Mean \overline{x}=\frac{\sum f_{i} x_{i}}{N}$

$\therefore \overline{x}=\frac{440}{20}$

$\therefore \overline{x}=22$

$\begin{aligned} S \cdot D \cdot=\sigma &=\sqrt{\frac{\sum f_{i} d_{i}^{2}}{N}-\left(\frac{\sum f_{i} d_{i}}{N}\right)^{2}} \times h \\ &=\sqrt{\frac{24}{20}-\left(\frac{-6}{20}\right)^{2}} \times 10 \\ &=10.54 \end{aligned}$

$\begin{aligned} \text { Coefficient of variance } &=\frac{\sigma}{x} \times 100 \\ &=\frac{10.54}{22} \times 100 \\ &=47.91 \end{aligned}$

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