sdrandom1 wrote:

First of all before evaluating any statements, we must make note that the given list of numbers has a standard deviation of 2. (Since each number differs from other by 2 units)

The standard deviation of the original set is not equal to 2. Remember that you calculate standard deviation by first computing the distance from each element to the mean, and in the given set, none of those distances is equal to 2. The mean of the set provided is equal to 10, and the distances from each element to the mean are:

9, 7, 5, 3, 1, 1, 3, 5, 7, 9

To compute the standard deviation, we square these distances, average those squares, and then take the square root, so the standard deviation is equal to:

\(\sqrt{\frac{9^2 + 7^2 + 5^2 + 3^2 + 1^2 + 1^2 + 3^2 + 5^2 + 7^2 + 9^2}{10}} = \sqrt{33} \approx 5.75\)

In any case, no matter what two elements are removed from the list 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, the standard deviation will change (though it's a bit of work to prove that), so you do not even need the statements to answer the question - the answer must be yes. I suppose that means the answer is D, but it doesn't seem to be a well-designed question.

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