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NDA 2025
Exam
NDA
Year
2025
Subject
Mathematics
Chapter
Statistics

NDA 2025 · Mathematics · Statistics

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

Consider the following for the two (02) items that follow:
The sum and the sum of squares of the observations corresponding to length XX (in cm) and weight YY (in gm) of 50 tropical tubers are given as ΣX=200\Sigma X = 200, ΣY=250\Sigma Y = 250, ΣX2=900\Sigma X^2 = 900 and ΣY2=1400\Sigma Y^2 = 1400.

Which one of the following statements is correct?

Options

  1. ACoefficient of variation of XX is strictly more than coefficient of variation of YY.
  2. BCoefficient of variation of XX is strictly less than coefficient of variation of YY.
  3. CCoefficient of variation of XX is same as coefficient of variation of YY.
  4. DCoefficient of variation cannot be determined from the given data.

Correct answer

A. Coefficient of variation of XX is strictly more than coefficient of variation of YY.

Step-by-step solution

Mean of XX, Xˉ=ΣXn=20050=4\bar{X} = \dfrac{\Sigma X}{n} = \dfrac{200}{50} = 4

Mean of YY, Yˉ=ΣYn=25050=5\bar{Y} = \dfrac{\Sigma Y}{n} = \dfrac{250}{50} = 5

Variance of XX, σX2=ΣX2n−(Xˉ)2=90050−42=18−16=2\sigma_X^2 = \dfrac{\Sigma X^2}{n} - (\bar{X})^2 = \dfrac{900}{50} - 4^2 = 18 - 16 = 2

Standard deviation of XX, σX=2\sigma_X = \sqrt{2}

Variance of YY, σY2=ΣY2n−(Yˉ)2=140050−52=28−25=3\sigma_Y^2 = \dfrac{\Sigma Y^2}{n} - (\bar{Y})^2 = \dfrac{1400}{50} - 5^2 = 28 - 25 = 3

Standard deviation of YY, σY=3\sigma_Y = \sqrt{3}

Coefficient of variation of XX, CVX=σXXˉ×100=24×100=252≈35.35%CV_X = \dfrac{\sigma_X}{\bar{X}} \times 100 = \dfrac{\sqrt{2}}{4} \times 100 = 25\sqrt{2} \approx 35.35\%

Coefficient of variation of YY, CVY=σYYˉ×100=35×100=203≈34.64%CV_Y = \dfrac{\sigma_Y}{\bar{Y}} \times 100 = \dfrac{\sqrt{3}}{5} \times 100 = 20\sqrt{3} \approx 34.64\%

Since 35.35%>34.64%35.35\% > 34.64\%, the coefficient of variation of XX is strictly more than the coefficient of variation of YY.

Answer: Coefficient of variation of XX is strictly more than coefficient of variation of YY.
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