The following are the marks obtained in a class test by a student: 10, 12, 15, 15, 18, 20, 20, 20, 23. The variance is?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 16.2
The variance is the mean of the squared deviations from the mean: \(\sigma^{2}=\frac{\sum(x-\bar{x})^{2}}{n}\). The mean is found first.
The mean (9 marks):
Sum of the nine marks: \(10+12+15+15+18+20+20+20+23=153\)
Mean, the sum divided by 9: \(\displaystyle\bar{x}=\frac{153}{9}=17\)
The squared deviations (\(x-17\), squared):
For the marks 10 and 12: \((-7)^{2}+(-5)^{2}=49+25=74\)
For the marks 15, 15 and 18: \(4+4+1=9\)
For the marks 20, 20, 20 and 23: \(9+9+9+36=63\)
Sum of all the squared deviations: \(74+9+63=146\)
The variance:
Squared deviations divided by the number of marks: \(\displaystyle\sigma^{2}=\frac{146}{9}=16.22\ldots\approx16.2\)