What is the standard deviation (SD) of the fo...

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What is the standard deviation (SD) of the four numbers p, q, r, and s?
(1) The sum of p, q, r, and s is 24.
(2) The sum of the squares of p, q, r, and s is 224.
• a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
• b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
• c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;
• d)
• e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Standard deviation = √Mean of squares of the numbers−square of mean of the numbers
Evaluating Statement (1) ALONE: The sum of p, q, r, and s is 24.
From the information in statement 1 we can find the mean of the four numbers to be 6 and the square of the mean of the numbers to be 36.
We need additional information to find the SD.
This statement does not provide any information about the mean of the squares of the numbers.
Statement 1 alone is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C, or E.
Evaluating Statement (2) ALONE: The sum of the squares of p, q, r, and s is 224.
Hence, the mean of the squares of the numbers is 56.
However, this statement does not provide any information about the square of the mean of the numbers.
Statement 2 alone is NOT sufficient.
Eliminate choice B. Choices narrow down to C and E.
Evaluating the statements together.
From statement 1 we know that the square of the means is 36.
From statement 2 we know that the mean of the squares is 56.
Using the formula,
Standard deviation = √Mean of squares of the numbers−square of mean of the numbers,
we can find the SD of the 4 numbers.
Statements together are sufficient. Choice C is the answer.

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