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NDA 2 2024 Maths, question 111

Topic: Statistics

Q111

Let ∑i=19xi2=855\sum _{i=1}^{9}x_{i}^{2}=855. If MM is the mean and σ\sigma is the standard deviation of x1,x2,…,x9x_{1},x_{2},\ldots ,x_{9}, then what is the value of M2+σ2M^{2}+\sigma^{2}?

  1. (a) 100100
  2. (b) 9595Correct answer
  3. (c) 9090
  4. (d) 8585

Solution.

Answer: (b) 9595

  1. Population variance is σ²=(Σxᵢ²)/9−M².
  2. Hence M²+σ²=855/9=95.
  3. The result depends only on the supplied sum of squares, not on the individual observations.