Multiple choice

The mean and variance of a data set are 10 and 25 respectively. If each observation is multiplied by 2 and then 5 is added, what is the new variance?

  1. 25

  2. 50

  3. 100

  4. 200
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C Correct answer
Explanation

If each observation is multiplied by a constant k, the variance is multiplied by k^2. Adding a constant does not change the variance. New variance = 25 * 2^2 = 25 * 4 = 100.

AI explanation

The variance of a data set is unaffected by adding a constant to every observation, but it is multiplied by the square of any constant. When each observation is multiplied by 2, the new variance is calculated as 2 squared times the original variance of 25. This gives a new variance of 4 multiplied by 25, which equals 100.

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