The following table gives the daily wages of workers in a factory. Compute the standard deviation and the coefficient of variation of the wages of the workers.

Wages (Rs)	125-175	175-225	225-275	275-325	325-375	375-425	425-475	475-525	525-575
Number of workers	2	22	19	14	3	4	6	1	1

Wages (Rs.)	Midpoint $(x_i)$	Frequency (f) (No. of workers)	$x_i^2$	$f_ix_i$	$f_ix_i^2$
125 - 175	150	2	22500	300	45,000
175 - 225	200	22	40000	4400	8,80,000
225 - 275	250	19	62500	4750	1187500
275 - 325	350	14	90000	4200	1260000
325 - 375	300	3	122500	1050	367500
375 - 425	350	4	160000	1600	640000
425 - 475	400	6	202500	2700	1215000
475 - 525	450	1	250000	500	250000
525 - 575	500	1	302500	550	302500
		72		20050	6147500

$\sum f = N = 72$

$\bar{x} = \dfrac{\sum f_ix_i}{N} = \dfrac{20050}{72} = 278.472222$

$\sum f_ix_i = 20050$

$\sum f_ix_i^2 = 6147500$

$\therefore$ Standard deviden $\sigma = \sqrt{\dfrac{\sum f_ix_i^2}{N} - \left(\dfrac{\sum f_ix_i}{N}\right)^2}$

$=\sqrt{\dfrac{6147500}{72} - \left(\dfrac{20050}{72}\right)^2}$

$=\sqrt{7835.165895}$

$\sigma = 88.51647245$

Coefficient of veriation $= \dfrac{\sigma}{\bar{x}}$

$= \dfrac{88.51647245}{278.4722222}$

$= 0.317864639$

$=0.32$