Q.
Find the variance of the data given below
Size of item
3.5
4.5
5.5
6.5
7.5
8.5
9.5
Frequency
3
7
22
60
85
32
8
| Size of item | 3.5 | 4.5 | 5.5 | 6.5 | 7.5 | 8.5 | 9.5 |
| Frequency | 3 | 7 | 22 | 60 | 85 | 32 | 8 |
BITSATBITSAT 2013
Solution:
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 $
| 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 |