| Age(in years) | 1 – 5 | 6 – 10 | 11 – 15 |
| Frequency | 3 | 5 | 2 |
Calculate the standard deviation of the distribution.
-
A.
1.10 -
B.
2.36 -
C.
3.50 -
D.
7.50
Correct Answer: Option C
Explanation
|
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)