Calculate standard deviation and co-efficient of variance of the following table:

marks below	5	10	15	20	25
No.of Students	6	16	28	38	46

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written 6.6 years ago by

teamques10 ★ 70k

Solution:

class	$x_{i}$	$f_{i}$	$f_{I}x_{I}$	$d_{I}=\frac{x_{i}-a}{h}$	$f_{i}d_{I}$	$d_{I}^{2}$	$f_{I}d_{I}^{2}$
0-5	2.5	6	15	-2	-12	4	24
5-10	7.5	10	75	-1	-10	1	10
10-15	12.5	12	150	0	0	0	0
15-20	17.5	10	175	1	10	1	10
20-25	22.5	8	180	2	16	4	32
		46	595		5		76

$Mean \overline{x}=\frac{\sum f_{i} x_{i}}{N}=\frac{595}{46}=12.935$

$S.D. =\sigma=\sqrt{\frac{\sum f_{i} d_{i}^{2}}{N}-\left(\frac{\sum f_{i} d_{i}}{N}\right)^{2}} \times h$

$(S . D .=\sigma=\sqrt{\frac{76}{46}-\left(\frac{4}{46}\right)^{2}} \times 5$

$S.D. $=\sigma=6.412$ $Coefficient of variance =\frac{\sigma}{\bar{x}} \times 100$ $$ =\frac{6.412}{12.935} \times 100 $$

$=49.57$

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