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

Answer: (C)

1.32

Answer 2

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

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