Multiple choice

A set of 20 numbers represents the height of 20 students of a particular class. The variance of the given 20 numbers is 8. Now, the height of each student is multiplied by 3. What is the new variance of the numbers?

  1. 64

  2. 72

  3. 87

  4. 65
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B Correct answer
Explanation

When each value in a data set is multiplied by a constant k, the variance is multiplied by k^2. Here, the original variance is 8 and the constant is 3, so the new variance is 8 * 3^2 = 8 * 9 = 72.

AI explanation

Using the properties of variance, when each observation in a dataset is multiplied by a constant k, the new variance becomes k squared times the original variance. Here, the heights are multiplied by 3, so the new variance is 3 squared times the original variance of 8. Calculating 9 times 8 gives a new variance of 72. The new variance is 72.

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