Multiple choice

If all the natural numbers between 1 and 20 are multiplied by 3, then what is the variance of the resulting series?

  1. 99.75

  2. 199.75

  3. 299.25

  4. 399.25
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C Correct answer
Explanation

The variance of the first n natural numbers is (n^2 - 1)/12. For n=20, variance = (400-1)/12 = 399/12 = 33.25. If each number is multiplied by k, the variance is multiplied by k^2. Here k=3, so new variance = 33.25 * 9 = 299.25.

AI explanation

The variance of the natural numbers from 1 to 20 is calculated using the formula (n^2 - 1) / 12, which gives (400 - 1) / 12 = 399 / 12 = 33.25. When each number in a series is multiplied by a constant k, the variance is multiplied by k^2. Multiplying the original variance of 33.25 by 3^2 gives 33.25 * 9 = 299.25.

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