| Age(in years) | 1 - 5 | 6 - 10 | 11 - 15 |
| Frequency | 3 | 5 | 2 |
Calculate the standard deviation of the distribution.
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Correct Answer: Option C
Explanation:
\(Mean (\bar {x}) = \frac{\sum fx}{\sum f} = \frac{75}{10} = 7.5\)
\(SD = \sqrt{\frac{\sum fd^{2}}{\sum f}}\)
= \(\sqrt{\frac{122.5}{10}}\)
= \(\sqrt{12.25} = 3.50\)
| 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 |
\(Mean (\bar {x}) = \frac{\sum fx}{\sum f} = \frac{75}{10} = 7.5\)
\(SD = \sqrt{\frac{\sum fd^{2}}{\sum f}}\)
= \(\sqrt{\frac{122.5}{10}}\)
= \(\sqrt{12.25} = 3.50\)