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UPSC NDA I 2025 Mathematics Paper

Question Numbers: 105-106

Consider the following for the two (02) items that follow:

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

ΣX=200

,ΣY=250,ΣX^{2}=900andΣY^{2}=1400

Question : 106 of 120

Marks: +1, -0

Which one of the following statements is correct?

Coefficient of variation of X is strictly more than coefficient of variation of Y.
Coefficient of variation of X is strictly less than coefficient of variation of Y
Coefficient of variation of X is same as coefficient of variation of Y.
Coefficient of variation cannot be determined from the given data.

Solution:

Concept:

The coefficient of variation (CV) measures relative variability. It is calculated as standard deviation divided by mean, multiplied by 100.

Explanation:

For X: Standard deviation

\sigma_X = \sqrt{2}

and mean

M_X = 50

. Thus,

C.V.(X) = \frac{\sqrt{2}}{50} \times 100 = 2\sqrt{2}

For Y: Standard deviation

\sigma_Y = \sqrt{3}

and mean

M_Y = 50

. Thus,

C.V.(Y) = \frac{\sqrt{3}}{50} \times 100 = 2\sqrt{3}

Since

\sqrt{2} < \sqrt{3}

, we get

2\sqrt{2} < 2\sqrt{3}

, meaning

C.V.(X) < C.V.(Y)

. Therefore, the coefficient of variation of X is strictly less than that of Y.

Answer:

Option B: Coefficient of variation of X is strictly less than coefficient of variation of Y.

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