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# A data set consists of three integers. What is the standard

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Re: A data set consists of three integers. What is the standard [#permalink]
Stmnt 1) {2,3,4} & {1,3,5} both sets with diff SD satisfy the statement

Stmnt2) {3,3,5} & {3,3,3} both sets with diff SD satisfy the statement

Stmnt 1 &2) Only{3,3,3} satisfy both statements and SD = 0
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Re: A data set consists of three integers. What is the standard [#permalink]
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sm021984 wrote:
A data set consists of three integers. What is the standard deviation of this data set?

(1) The average (arithmetic mean) and the median are both 3.
(2) At least two of the numbers are 3.

Target question: What is the standard deviation of the 3-integer data set?

Statement 1: The average (arithmetic mean) and the median are both 3
Let's TEST some values.
There are several sets that satisfy statement 1. Here are two:
Case a: {3, 3, 3}. Notice that the median and mean both equal 3. In this case, the standard deviation is 0
Case b: {1, 3, 5}. Notice that the median and mean both equal 3. In this case, the standard deviation is NOT 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: At least two of the numbers are 3
There are several sets that satisfy statement 1. Here are two:
Case a: {3, 3, 3}. In this case, the standard deviation is 0
Case b: {3, 3, 100}. In this case, the standard deviation is NOT 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that the average (arithmetic mean) and the median are both 3. This means the 3 numbers MUST ADD to 9
Statement 2 tells us that at least two of the numbers are 3.
If two of the numbers are 3's AND all three numbers must add to 9, then all three numbers MUST be 3's
That is, the set MUST be {3, 3, 3}, in which case, the standard deviation is 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

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Re: A data set consists of three integers. What is the standard [#permalink]
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Re: A data set consists of three integers. What is the standard [#permalink]
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