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Which of the following must be true of Set S?

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Which of the following must be true of Set S?

by gmattesttaker2 » Sat Jan 11, 2014 7:18 pm
Hello,

Can you please assist with this:

Set S is made up of all integers n such that n is a multiple of 5 and -20 less than or equal to n less than or equal to 60, which of the following must be true of Set S?


1) If each term is multiplied by 3, its average, median and standard deviation will change.

2) The absolute value of the terms of set S will have the same standard deviation.

3) If 6 is added to each of the terms in set S, it's average (arithmetic mean) and median will change but not its standard deviation.

A) I only
B) I and II only
C) II and III only
D) III only
E) I and III only

OA: E

Thanks a lot,
Sri
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by Uva@90 » Sat Jan 11, 2014 7:43 pm
gmattesttaker2 wrote:Hello,

Can you please assist with this:

Set S is made up of all integers n such that n is a multiple of 5 and -20 less than or equal to n less than or equal to 60, which of the following must be true of Set S?


1) If each term is multiplied by 3, its average, median and standard deviation will change.

2) The absolute value of the terms of set S will have the same standard deviation.

3) If 6 is added to each of the terms in set S, it's average (arithmetic mean) and median will change but not its standard deviation.

A) I only
B) I and II only
C) II and III only
D) III only
E) I and III only

OA: E

Thanks a lot,
Sri
Hi Sri,
Is question stated as, n is multiple of 5 and ,-20 <= n <= 60 ?
I assume as this,
So set should be {-20,-15,-10,.........50,55,60}

As we know that,
If we add or subtract a constant to each term in a set Mean will increase or decrease by the same constant SD will not change.

So, option 3 is correct.
Eliminate A and B

Consider the second point, 'The absolute value of the terms of set S will have the same standard deviation.'

It will be true if set has all positive values,
But set has negative values too.
Hence Option 2 is Incorrect. Eliminate C

Consider Option 1.
For example consider easy numbers,
1,2,3 here SD is 1
Multiply by 3, then set is 3,6,9. Here SD is 3
Hence Option 1 is correct.

Ans is E

Regards,
Uva.
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by gmattesttaker2 » Tue Jan 14, 2014 10:35 pm
Uva@90 wrote:
gmattesttaker2 wrote:Hello,

Can you please assist with this:

Set S is made up of all integers n such that n is a multiple of 5 and -20 less than or equal to n less than or equal to 60, which of the following must be true of Set S?


1) If each term is multiplied by 3, its average, median and standard deviation will change.

2) The absolute value of the terms of set S will have the same standard deviation.

3) If 6 is added to each of the terms in set S, it's average (arithmetic mean) and median will change but not its standard deviation.

A) I only
B) I and II only
C) II and III only
D) III only
E) I and III only

OA: E

Thanks a lot,
Sri
Hi Sri,
Is question stated as, n is multiple of 5 and ,-20 <= n <= 60 ?
I assume as this,
So set should be {-20,-15,-10,.........50,55,60}

As we know that,
If we add or subtract a constant to each term in a set Mean will increase or decrease by the same constant SD will not change.

So, option 3 is correct.
Eliminate A and B

Consider the second point, 'The absolute value of the terms of set S will have the same standard deviation.'

It will be true if set has all positive values,
But set has negative values too.
Hence Option 2 is Incorrect. Eliminate C

Consider Option 1.
For example consider easy numbers,
1,2,3 here SD is 1
Multiply by 3, then set is 3,6,9. Here SD is 3
Hence Option 1 is correct.

Ans is E

Regards,
Uva.

Hello Uva,

Thank you very much for your excellent explanation. I just had a question about the calculation of Standard Deviation. For the following:
Consider Option 1.
For example consider easy numbers,
1,2,3 here SD is 1
Multiply by 3, then set is 3,6,9. Here SD is 3
I tried to calculate Standard Deviation for 1,2,3 as follows:

SD = sq. root ( ( (1-2)^2 + (2-2)^2 + (3-2)^2 )/ 3 ) = sq. root ( 2 / 3)

For 3,6,9 I got SD = sq. root ( 6 )

I was just wondering where I was going wrong. Thanks for all your help.

Best Regards,
Sri
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by Matt@VeritasPrep » Wed Jan 15, 2014 12:22 pm
You and Uva are both right: 3 is the SAMPLE standard deviation, while √6 is the POPULATION standard deviation. These are different measures that are used in different situations. Here's a brief primer on the topic.

That said, you are correct (IIRC) that the GMAT uses the POPULATION standard deviation, which here would be √6, although I don't think there are any GMAT questions that depend on your making the distinction between the two.
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by gmattesttaker2 » Wed Jan 15, 2014 6:44 pm
Matt@VeritasPrep wrote:You and Uva are both right: 3 is the SAMPLE standard deviation, while √6 is the POPULATION standard deviation. These are different measures that are used in different situations. Here's a brief primer on the topic.

That said, you are correct (IIRC) that the GMAT uses the POPULATION standard deviation, which here would be √6, although I don't think there are any GMAT questions that depend on your making the distinction between the two.
Hello Matt,

Thanks a lot.

Best Regards,
Sri
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