Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Join a free live webinar and find out which skills will get you to the top, and what you can do to develop them. Save your spot today! Tuesday, July 16th at 3 pm PST

The Competition Continues - Game of Timers is a team-based competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th

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

Show Tags

27 Jun 2007, 03:59

1

1

71

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

30% (01:50) correct 70% (01:28) wrong based on 672 sessions

HideShow timer Statistics

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

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

Show Tags

29 Aug 2016, 12:01

10

Top Contributor

13

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

For GMAT purposes, Standard Deviation (SD) can often be thought of as "the average distance the data points are away from the mean."

So, with {0, 2, 4, 6, 8}, the mean is 4. 0 is 4 units away from the mean of 4. 2 is 2 units away from the mean of 4. 4 is 0 units away from the mean of 4. 6 is 2 units away from the mean of 4. 8 is 4 units away from the mean of 4.

So, the SD can be thought of as the average of 4, 2, 0, 2, and 4. The average of these values is 2.4, so we'll say that the SD is about 2.4

Note: This, of course, isn't 100% accurate, but it's all you should really need for the GMAT.

Okay, so which pair of new numbers, when added to the original 5, numbers will yield a new SD that is closest to 2.4?

Well, to begin, it's useful to notice that each pair consists of numbers that are equidistant from the original mean of 4. For example, in answer choice A, -1 is 5 units less than 4, and 6 is 5 units more than 4. As such, add the two values in each answer choice will yield a mean of 4.

Okay, let's see what happens if we add -1 and 9 (answer choice A). Well, -1 is 5 units away from the mean of 4, and 9 is 5 units away from the mean of 4. So, 5 and 5 will be added to 4, 2, 0, 2, and 4 to get a new SD. As you can see, this will result in a much larger SD.

Now, let's examine D (2 and 6) Well, 2 is 2 units away from the mean of 4, and 6 is 2 units away from the mean. So, we'll be adding 2 and 2 to the five original differences of 4, 2, 0, 2, and 4. Since the average of 4, 2, 0, 2, and 4 is 2.4, adding differences of 2 and 2 should have the least effect on the original SD.

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

Re: A set of data consists of the following 5 numbers: 0,2,4,6, and 8.
[#permalink]

Show Tags

17 Apr 2010, 06:32

utin 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

as per rule: standard deviation is least affect by adding new element if the newly added elements are at equal distance from the mean of the set. so here mean is 4 => if 2 and 6 are added then SD will be least affected. hope this will help

Re: A set of data consists of the following 5 numbers: 0,2,4,6, and 8.
[#permalink]

Show Tags

Updated on: 17 Apr 2010, 18:31

1

2

gurpreetsingh wrote:

if that is true then why not 3 and 5?

IMO it should be 4 and 4, as mean = new number, the change in deviation will be zero

yes, i missed one thing, to have minimum impact on SD, new values should be at equal distance from the mean and if new numbers are more farther from the mean, less impact will be on SD. if u look at the formula for SD, it will be more clear. if the values are same in that case in formula numerator will add 0 values for the the number(as mean will not change). however, denominator will increase by 2, thus the SD will be reduced considerably. hope this will help

Originally posted by einstein10 on 17 Apr 2010, 13:02.
Last edited by einstein10 on 17 Apr 2010, 18:31, edited 1 time in total.

Re: A set of data consists of the following 5 numbers: 0,2,4,6, and 8.
[#permalink]

Show Tags

Updated on: 17 Apr 2010, 13:42

sandeep25398 wrote:

gurpreetsingh wrote:

if that is true then why not 3 and 5?

IMO it should be 4 and 4, as mean = new number, the change in deviation will be zero

yes, i missed one thing, to have minimum impact on SD, new values should be at equal distance from the mean and if new numbers are more farther from the mean, less impact will be on SD. if u look at the formula for SD, it will be more clear. if the values are same in that case in formula denominator will add 0 values for the the number(as mean will not change). however, numerator will increase by 2, thus the SD will be reduced considerably. hope this will help

oh yea its 2 am here...lol...out of senses i guess and u also seems to be....

lol pls change numerator with denominator

PS; I got your point.

If the number are too far or too close to the mean the change will be bigger. D is apparently not too far and too close to the means as compared to others.
_________________

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

Show Tags

30 Aug 2013, 09:12

2

3

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]

Show Tags

11 Mar 2018, 02:33

1

1

Given: {0,2,4,6,8} Mean : 4 Let us not exact calculate S.D., we will stop one step before calculation \(((0 - 4)^2 + (2-4)^2 + (4-4)^2 + (6-4)^2 + (8-4)^2)\) / 5 = 40/5 = 8

Let A = \((0 - 4)^2 + (2-4)^2 + (4-4)^2 + (6-4)^2 + (8-4)^2\)

Examining the options, options are given thankfully so that mean remains the same, after adding the options. (reducing our burden to calc mean again)

Option 1: -1 and 9 \(( A + (-1-4)^2 + (9-4)^2)/7 => (40 + 25 + 25) / 7\)= well over 8

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

Show Tags

07 Jul 2018, 07:46

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

I chose answer C here, can anyone explain why C is wrong. I understand to have lesser impact on SD points added should be far away from mean. In that case along with D, E also explains the same thing. Why we rejected E?
_________________

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

Show Tags

07 Jul 2018, 08:53

Cbirole wrote:

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

I chose answer C here, can anyone explain why C is wrong. I understand to have lesser impact on SD points added should be far away from mean. In that case along with D, E also explains the same thing. Why we rejected E?

Hello Cbirole. The SD of the original set of 5 is square root of 8 (I’m sending this from my phone, so I can’t the use the square root symbol). Thus you are looking or an answer that yields either the sq. root of 8 or that which is closest. Evaluating the answers individually, you will find by adding 0,8 to the original set yields the sq. root of 8. Hope that helps. As for trying to short-cut it through theoretical approximation, someone smarter than me in the SD field will have to step up.

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

Show Tags

09 Jul 2018, 06:26

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

What exactly are variations? Could you please elaborate on that?

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

Show Tags

19 Aug 2018, 01:20

lets start by finding mean of given data, its 4 now if we add each option one by one in the given series we will have same mean (4) lets calculate SD of 5 given numbers SD = (16+4+0+4+16)/5 = 40/5 = 8

it means we are looking for adding 2 numbers in the given series of 5 numbers to have SD very close to 8. lets plug in all the options one by one to calculate SD of 7 numbers.

A) ((5)^2 + 40 + (-5)^2)/7 = 12.--- B) (0+40+0)/7 = 5.--- C) (1+40+1)/7 = 6 D) (4+40+4)/7 = ~7 E) (16+40+16)/7 = 10.---

As Option (D) is very close to 8 so D is the answer _________________

Hasnain Afzal

"When you wanna succeed as bad as you wanna breathe, then you will be successful." -Eric Thomas

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

Show Tags

01 Apr 2019, 08:10

GMATPrepNow wrote:

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

For GMAT purposes, Standard Deviation (SD) can often be thought of as "the average distance the data points are away from the mean."

So, with {0, 2, 4, 6, 8}, the mean is 4. 0 is 4 units away from the mean of 4. 2 is 2 units away from the mean of 4. 4 is 0 units away from the mean of 4. 6 is 2 units away from the mean of 4. 8 is 4 units away from the mean of 4.

So, the SD can be thought of as the average of 4, 2, 0, 2, and 4. The average of these values is 2.4, so we'll say that the SD is about 2.4

Note: This, of course, isn't 100% accurate, but it's all you should really need for the GMAT.

Okay, so which pair of new numbers, when added to the original 5, numbers will yield a new SD that is closest to 2.4?

Well, to begin, it's useful to notice that each pair consists of numbers that are equidistant from the original mean of 4. For example, in answer choice A, -1 is 5 units less than 4, and 6 is 5 units more than 4. As such, add the two values in each answer choice will yield a mean of 4.

Okay, let's see what happens if we add -1 and 9 (answer choice A). Well, -1 is 5 units away from the mean of 4, and 9 is 5 units away from the mean of 4. So, 5 and 5 will be added to 4, 2, 0, 2, and 4 to get a new SD. As you can see, this will result in a much larger SD.

Now, let's examine D (2 and 6) Well, 2 is 2 units away from the mean of 4, and 6 is 2 units away from the mean. So, we'll be adding 2 and 2 to the five original differences of 4, 2, 0, 2, and 4. Since the average of 4, 2, 0, 2, and 4 is 2.4, adding differences of 2 and 2 should have the least effect on the original SD.

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

Show Tags

28 May 2019, 08:35

A very important question to understand Standard deviation. The 5 numbers on average are 2.4 points away from the mean...ie 12/5 =2.4.

Now we need to find a pair of 2 numbers such that their average deviation from mean is closest to 2.4. Or the sum of their deviation is closest to 4.8

Following are the average deviation in case of each option A) -1, 9 --> Sum of deviation from mean(4) is equal to (5+5=10) B) 4, 4 --> Sum of deviation from mean(4) is equal to (0+0=0) C) 3,5 --> Sum of deviation from mean(4) is equal to (1+1=2) D) 2,6 --> Sum of deviation from mean(4) is equal to (2+2=4) Closest to 4.8 . Hence, this is the correct answer E) 0,8 --> Sum of deviation from mean(4) is equal to (4+4=8)
_________________