COMEDK · Maths · 29. Statistics
Consider the first 10 natural numbers. If we multiply each number by \(-\)1 and add 1 to each number, the variance of the numbers so obtained is
- A 8.25
- B 6.5
- C 3.87
- D 2.87
Answer & Solution
Correct Answer
(A) 8.25
Step-by-step Solution
Detailed explanation
Let the original set of numbers be \(X = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}\). The variance of the first \(n\) natural numbers is given by the formula \(Var(X) = \dfrac{n^2 - 1}{12}\). For \(n = 10\), \(Var(X) = \dfrac{10^2 - 1}{12} = \dfrac{99}{12} = 8.25\). The new set of…
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