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NDA 1 2025 Maths, question 105

Topic: Statistics

Passage · Q105 to Q106

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 ∑X=200\sum X = 200, ∑Y=250\sum Y = 250, ∑X2=900\sum X^{2} = 900 and ∑Y2=1400\sum Y^{2} = 1400.

Q105

Which one of the following is correct?

  1. (a) Variance (X) > Variance (Y)
  2. (b) Variance (X) < Variance (Y)Correct answer
  3. (c) Variance (X) = Variance (Y)
  4. (d) Cannot be determined from the given data

Solution.

Answer: (b) Variance (X) < Variance (Y)

  1. The means are Xˉ=200/50=4\bar{X} = 200/50 = 4 and Yˉ=250/50=5\bar{Y} = 250/50 = 5.
  2. Using variance =∑x2/N−xˉ2= \sum x^{2}/N - {\bar{x}}^{2}, obtain Var(X)=900/50−16=2Var(X) = 900/50 - 16 = 2 and Var(Y)=1400/50−25=3Var(Y) = 1400/50 - 25 = 3.
  3. Thus the numerical variance of X is smaller in the specified units.