The marks obtained by 10 students in a test are as follows: 3, 7, 6, 2, 8, 5, 9, 1, 4 and 10. Find the variance.
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Correct Answer: Option A
Explanation:
Mean \(\bar{x}\) = \(\frac{3 + 7 + 6 + 2 + 8 + 5 + 9 + 1 + 4 + 10}{10} \)
= \(\frac{55}{10} = 5.50\)
Variance = \(\frac{\sum (x - \bar{x})^{2}}{n}\)
= \(\frac{82.5}{10}\)
= 8.25
Mean \(\bar{x}\) = \(\frac{3 + 7 + 6 + 2 + 8 + 5 + 9 + 1 + 4 + 10}{10} \)
= \(\frac{55}{10} = 5.50\)
| \(x\) | 3 | 7 | 6 | 2 | 8 | 5 | 9 | 1 | 4 | 10 | Total |
| \(x - \bar{x}\) | -2.5 | 1.5 | 0.5 | -3.5 | 2.5 | -0.5 | 3.5 | -4.5 | -1.5 | 4.5 | |
| \((x - \bar{x})^{2}\) | 6.25 | 2.25 | 0.25 | 12.25 | 6.25 | 0.25 | 12.25 | 20.25 | 2.25 | 20.25 | 82.5 |
Variance = \(\frac{\sum (x - \bar{x})^{2}}{n}\)
= \(\frac{82.5}{10}\)
= 8.25