Q.
The variance of the following frequency distribution is
Class Interval
0 - 6
6 - 12
12 - 18
18 - 24
24 - 30
Frequency
10
8
6
4
2
| Class Interval | 0 - 6 | 6 - 12 | 12 - 18 | 18 - 24 | 24 - 30 |
| Frequency | 10 | 8 | 6 | 4 | 2 |
TS EAMCET 2020
Solution:
Cl
$f_i$
$x_i$
$f_ix_i$
$x_i^2$
$f_ix_i^2$
0 - 6
10
3
30
9
90
6 -12
8
9
72
81
648
12 - 18
6
15
90
225
1350
18 - 24
4
21
84
441
1764
24 - 30
2
27
54
729
1458
Total
$\sum f_i = 30$
$\sum f_ixi = 330$
$\sum f_ix_i^2 = 5310$
$\therefore $ Variance $=\frac{1}{N} \sum f_{i} x_{i}^{2}-\left(\frac{\sum f_{i} x_{i}}{N}\right)^{2}$
$=\frac{1}{30} \times 5310-\left(\frac{330}{30}\right)^{2}$
$=177-121=56$
| Cl | $f_i$ | $x_i$ | $f_ix_i$ | $x_i^2$ | $f_ix_i^2$ |
|---|---|---|---|---|---|
| 0 - 6 | 10 | 3 | 30 | 9 | 90 |
| 6 -12 | 8 | 9 | 72 | 81 | 648 |
| 12 - 18 | 6 | 15 | 90 | 225 | 1350 |
| 18 - 24 | 4 | 21 | 84 | 441 | 1764 |
| 24 - 30 | 2 | 27 | 54 | 729 | 1458 |
| Total | $\sum f_i = 30$ | $\sum f_ixi = 330$ | $\sum f_ix_i^2 = 5310$ |