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The sum of squares and the products of every pair of n non-negative real numbers X1,...

The sum of squares and the products of every pair of n non-negative real numbers X1, . .., Xn are known, however X1, ... , Xn are not known. Based on this information

(A) both the mean and the standard deviation of these numbers can be determined.

(B) neither the mean nor the standard deviation of these numbers can be determined.

(C) the mean can not be determined but the standard deviation of these numbers can be determined.

(D) the mean can be determined but the standard deviation of these numbers can not be determined.

Math   Statistics-And-Probability   
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Answer #1

The formula of obtaining mean is:

where, denotes the sum of "n" non negative real numbers.

The formula of obtaining standard deviation is:

where, denotes the sum of squares of "n" non negative real numbers.

Since, is not known, therefore, the mean value cannot be obtained.

And since, Mean cannot be obtained, therefore, Standard deviation also cannot be obtained as in the formula of the standard deviation, the mean value is required.

Thus, option B) is correct, that is "neither the mean nor the standard deviation of these numbers can be determined".

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