NDA 1 2024 Maths, question 120

Topic: Statistics

Passage · Q119 to Q120

The marks obtained by $10$ students in a Statistics test are $24,47,18,32,19,15,21,35,50$ and $41$ .

Q120

What is the variance of the largest five observations ?

(a) $14.6$
(b) $21.8$
(c) $25.2$
(d) $46.8$ Correct answer

Solution.

Answer: (d) $46.8$

For 32, 35, 41, 47 and 50, the mean is 41.
Squared deviations sum to 81 + 36 + 0 + 36 + 81 = 234.
The variance of these five observations is 234/5 = 46.8; divide by 5, not the sample-estimator divisor 4.