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

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sm021984
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A data set consists of three integers. What is the standard [#permalink] New post   22 Jul 2011, 15:02
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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.


Can we use negative numbers to calculate mean/median in such problems ?
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piyatiwari
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Re: Statistics [#permalink] New post   22 Jul 2011, 17:13
Why would you use negative numbers?

In Stmnt 1. average of 3 numbers is 3 -> so at least one number has to be +ve
In Stmnt 2. two of the numbers are +ve.
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Re: Statistics [#permalink] New post   23 Jul 2011, 22:19
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We can't rule out negative numbers in advance, but we don't need them.

(1) Since the median equals the mean, and we have only three numbers, we know that the two other numbers must be equidistant from the mean. So, to list a few examples, we could have:

3,3,3
2,3,4
0,3,6
and yes, -5,3,11

These all have different standard deviations. Insufficient.

(2) At least 2 of the numbers are 3, but the third number could be anything:

3,3,3
0,3,3
3,3,55
-1,000,047, 3, 3

. . . etc. These all have different standard deviations. Insufficient.

(1&2) Two of the numbers are 3, and the end numbers must be equidistant from the mean/median.

If the median and one other number are 3, then the third number would also have to be 3 to be equidistant from the median.

If the ends are both 3, the median would have to be 3. After all, there's nothing in between 3 and 3. :)

The set is 3,3,3. The SD is 0. Sufficient.
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Re: A data set consists of three integers. What is the standard [#permalink] New post   30 Jul 2017, 05:04
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] New post   31 May 2018, 19:06
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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

Answer: C

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Re: A data set consists of three integers. What is the standard [#permalink] New post   30 Sep 2021, 02:03
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