NDA 1 2025 Maths, question 106

Topic: Statistics

Passage · Q105 to Q106

The sum and the sum of squares of the observations corresponding to length $X$ (in cm) and weight $Y$ (in gm) of 50 tropical tubers are given as $\sum X = 200$ , $\sum Y = 250$ , $\sum X^{2} = 900$ and $\sum Y^{2} = 1400$ .

Q106

Which one of the following statements is correct?

(a) Coefficient of variation of X is strictly more than coefficient of variation of Y.Correct answer
(b) Coefficient of variation of X is strictly less than coefficient of variation of Y.
(c) Coefficient of variation of X is same as coefficient of variation of Y.
(d) Coefficient of variation cannot be determined from the given data.

Solution.

Answer: (a) Coefficient of variation of X is strictly more than coefficient of variation of Y.

From the means and variances, $CV_{X} = 100\sqrt{2}/4$ and $CV_{Y} = 100\sqrt{3}/5$ .
Both are positive, so compare their squares without approximating: $2/16 = 1/8 > 3/25$ .
Therefore $CV_{X} > CV_{Y}$ (about 35.36% versus 34.64%).