Question

Find the variance of the data given below

Occurance $(x_i)$	Frequency $(f_i)$	Freq $\ast (x_i)$	$(x_i-mean)$	$(x_i-mean)^2$	$f_i(x_i-mean)^2$
3.5	3	10.5	-3.59	12.887	38.661
4.5	7	31.5	-2.59	6.707	46.952
5.5	22	121	121	2.528	55.609
6.5	60	390	-0.59	0.348	20.876
7.5	85	637.5	0.41	0.168	14.298
8.5	32	272	1.41	1.988	63.632
9.5	8	76	2.41	5.809	46.47
Total	217	1538.5	-	-	286.498

• A. 1.29
• B. 2.19
• C. 1.32
• D. None of these

Answer 1

The Correct Option is C

Occurance $(x_i)$	Frequency $(f_i)$	Freq $\ast (x_i)$	$(x_i-mean)$	$(x_i-mean)^2$	$f_i(x_i-mean)^2$
3.5	3	10.5	-3.59	12.887	38.661
4.5	7	31.5	-2.59	6.707	46.952
5.5	22	121	121	2.528	55.609
6.5	60	390	-0.59	0.348	20.876
7.5	85	637.5	0.41	0.168	14.298
8.5	32	272	1.41	1.988	63.632
9.5	8	76	2.41	5.809	46.47
Total	217	1538.5	-	-	286.498

$\sigma^{2} = \frac{\sum f_{i}\left(x_{i} -\bar{x}\right)^{2}}{\sum f_{i}} = \frac{286.49}{217} $
$= 1.32 $