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A set of data consists of the following 5 numbers: 0, 2, 4 [#permalink]
27 Jun 2007, 02:59

2

This post was BOOKMARKED

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A

B

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D

E

Difficulty:

55% (hard)

Question Stats:

27% (02:23) correct
73% (00:56) wrong based on 105 sessions

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

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

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.

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.

Re: A set of data consists of the following 5 numbers: 0,2,4,6, [#permalink]
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

Re: A set of data consists of the following 5 numbers: 0, 2, 4 [#permalink]
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