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A set of data consists of the following 5 numbers: 0, 2, 4

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A set of data consists of the following 5 numbers: 0, 2, 4 [#permalink] New post 27 Jun 2007, 02:59
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A set of data consists of the following 5 numbers: 0, 2, 4, 6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?

A. -1 and 9
B. 4 and 4
C. 3 and 5
D. 2 and 6
E. 0 and 8
[Reveal] Spoiler: OA
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 [#permalink] New post 27 Jun 2007, 09:45
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D

From the given #s it is clear 4 is mean(average) of both sets.
If the variations of the sets are equal or close then their Stand Deviations are equal/close to each other too.

Variation of 1-set (5 #s) is 40/5=8
so Varition of set2 (7 #s) must be around 8 too, thus (40+ x)/7= around 8

x must be close to 16 so only D satisfies this value: (4-2)^2 +(4-6)^2=8
U can check others:
A) (4+1)^2+(4-9)^2=50
B) (4-4)^2+(4-4)^2=0
c) (4-3)^2+(4-5)^2=2
D) (4-2)^2 +(4-6)^2=8
E) (4-0)^2+(4-8)^2=32
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 [#permalink] New post 27 Jun 2007, 10:30
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UMB wrote:
D

From the given #s it is clear 4 is mean(average) of both sets.
If the variations of the sets are equal or close then their Stand Deviations are equal/close to each other too.

Variation of 1-set (5 #s) is 40/5=8
so Varition of set2 (7 #s) must be around 8 too, thus (40+ x)/7= around 8

x must be close to 16 so only D satisfies this value: (4-2)^2 +(4-6)^2=8
U can check others:
A) (4+1)^2+(4-9)^2=50
B) (4-4)^2+(4-4)^2=0
c) (4-3)^2+(4-5)^2=2
D) (4-2)^2 +(4-6)^2=8
E) (4-0)^2+(4-8)^2=32


This is a good explanation. You can also do it by looking at the numbers and using your common sense about standard deviation.

The average of the first list is 4 and the number deviate from 4 evenly. what i mean by that is, the next set of numbers (2,6) are both 2 away from 4, and the next set after that (0,8) are both 4 away from 4.

To have a similar deviation, we want the next set to look similar.

-1 and 9 will stretch the outter limits of the list, so that will increase the standard deviation significantly.
4 and 4 will add too much weight to the center of the list. It'll decrease the standard deviation.
3 and 5 may be right
2 and 6 may be right
0 and 8 will add weight to the outter limits again, and stretch the deviation.

So it's a toss up between (3 and 5) and (2 and 6). And my educated guess is on 2 and 6, since basically comes in right in the center of the previous standard deviation, it should change it the least.

For the record, I have never taught the standard deviation formula to any student of mine. I find it to be unnecessary for the GMAT when good, conceptual thinking can get you through.
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Re: PS: Stand. Deviation [#permalink] New post 24 Mar 2008, 07:54
thats exactly how i did it.

i think the trap for many ppl is choosing 4,4.
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Re: [#permalink] New post 23 Oct 2011, 04:55
ian7777 wrote:
UMB wrote:
D

From the given #s it is clear 4 is mean(average) of both sets.
If the variations of the sets are equal or close then their Stand Deviations are equal/close to each other too.

Variation of 1-set (5 #s) is 40/5=8
so Varition of set2 (7 #s) must be around 8 too, thus (40+ x)/7= around 8

x must be close to 16 so only D satisfies this value: (4-2)^2 +(4-6)^2=8
U can check others:
A) (4+1)^2+(4-9)^2=50
B) (4-4)^2+(4-4)^2=0
c) (4-3)^2+(4-5)^2=2
D) (4-2)^2 +(4-6)^2=8
E) (4-0)^2+(4-8)^2=32


This is a good explanation. You can also do it by looking at the numbers and using your common sense about standard deviation.

The average of the first list is 4 and the number deviate from 4 evenly. what i mean by that is, the next set of numbers (2,6) are both 2 away from 4, and the next set after that (0,8) are both 4 away from 4.

To have a similar deviation, we want the next set to look similar.

-1 and 9 will stretch the outter limits of the list, so that will increase the standard deviation significantly.
4 and 4 will add too much weight to the center of the list. It'll decrease the standard deviation.
3 and 5 may be right
2 and 6 may be right
0 and 8 will add weight to the outter limits again, and stretch the deviation.

So it's a toss up between (3 and 5) and (2 and 6). And my educated guess is on 2 and 6, since basically comes in right in the center of the previous standard deviation, it should change it the least.

For the record, I have never taught the standard deviation formula to any student of mine. I find it to be unnecessary for the GMAT when good, conceptual thinking can get you through.


Great explanation.
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Re: A set of data consists of the following 5 numbers: 0,2,4,6, [#permalink] New post 30 Aug 2013, 08:12
The above method explains it well , and if you are short of time and need to make an educated guess , this works perfect.

If you are in for some calculations , this is how I got to it

mean = 4
sd = \sqrt{8} = 2.8


Expected values for the SD to not change are - One value below SD from mean is (4 - 2.8) = 1.2 , and one value above SD is (4 + 2.8) = 6.8
This would mean , adding 1.2 ans 6.8 would have no impact on the SD . SD remains the same when these two numbers are added. Now for SD to change the least , we need to add two values that are closest to these two values.

Hence any two values that are closest to 1.2 and 6.8 would change the SD , the least.

1. -1 , 9
distance between (1,9) and (1.2 and 6.8) is 2.2 and 2.2

2. 4 , 4
distance etween (4,4) and (1.2 , 6.8) is 2.8 and 2.8

3. 3 , 5
Distance is - 1.8 and 1.8

4. 2 , 6
Distance is - 0.8 and 0.8

5. 0 , 8
Distnace is - 1.2 and 1.2

Hence from above , we see that adding 2 and 6 , results in a value that would change the SD to the least. Hence D

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Re: A set of data consists of the following 5 numbers: 0, 2, 4 [#permalink] New post 31 Aug 2013, 04:33
Expert's post
GK_Gmat wrote:
A set of data consists of the following 5 numbers: 0, 2, 4, 6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?

A. -1 and 9
B. 4 and 4
C. 3 and 5
D. 2 and 6
E. 0 and 8


Discussed here: ps-questions-about-standard-deviation-85897-20.html#p668837
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Re: A set of data consists of the following 5 numbers: 0, 2, 4   [#permalink] 31 Aug 2013, 04:33
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