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SD

by shashank.ism » Tue Feb 09, 2010 12:22 pm
What is the standard deviation (SD) of the four numbers p, q, r, 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

OA is C
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Source: — Data Sufficiency |
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by harsh.champ » Tue Feb 09, 2010 12:25 pm
shashank.ism wrote:What is the standard deviation (SD) of the four numbers p, q, r, 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

OA is C
The question asks one to find the standard deviation of four numbers.

Standard deviation = SQRT((mean of squares of the numbers - square of the mean of the numbers))

Statement (1) gives the information about the sum of the 4 numbers.

From this information we can find the mean of the four numbers is 6 and the square of the mean of the numbers is 36.

However, this statement does not provide any information about the mean of the squares of the numbers.

Hence, statement (1) alone is not sufficient.

Statement (2) gives the sum of the squares of the 4 numbers.

Hence, the mean of the squares of the numbers is 61.

However, this statement does not provide any information about the square of the mean of the numbers.

Hence, statement (2) alone is not sufficient.

When the information provided in the two statements are combined, one can find the standard deviation of the four numbers. Hence, answer is choice (C ).
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