| Age(in years) |
1 - 5 |
6 - 10 |
11 - 15 |
| Frequency |
3 |
5 |
2 |
Calculate the standard deviation of the distribution.
|
Age
(years)
|
Freq
(f)
|
Mid-value
(x)
|
fx |
\(d = (x - \bar{x})\) |
\(d^{2}\) |
\(fd^{2}\) |
| 1 - 5 |
3 |
3 |
9 |
- 4.5 |
20.25 |
60.75 |
| 6 - 10 |
5 |
8 |
40 |
0.5 |
0.25 |
1.25 |
| 11 - 15 |
2 |
13 |
26 |
5.5 |
30.25 |
60.5 |
| \(\sum =\) |
10 |
|
75 |
|
|
122.5 |
\(Mean (\bar {x}) = \frac{\sum fx}{\sum f} = \frac{75}{10} = 7.5\)
\(SD = \sqrt{\frac{\sum fd^{2}}{\sum f}}\)
= \(\sqrt{\frac{122.5}{10}}\)
= \(\sqrt{12.25} = 3.50\)