Jul 21 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes Jul 20 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jul 26 08:00 AM PDT  09:00 AM PDT The Competition Continues  Game of Timers is a teambased 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 Jul 27 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56304

Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a
[#permalink]
Show Tags
22 May 2019, 23:26
Question Stats:
55% (01:05) correct 45% (01:09) wrong based on 38 sessions
HideShow timer Statistics
Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a number 15 is included in the series, then which of the following will change? I. Median II. Mode III. Standard deviation A. I only B. II only C. III only D. I and III only E. I, II and III
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



ISB School Moderator
Joined: 08 Dec 2013
Posts: 530
Location: India
Concentration: Nonprofit, Sustainability
WE: Operations (NonProfit and Government)

Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a
[#permalink]
Show Tags
Updated on: 23 May 2019, 01:50
Bunuel wrote: Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a number 15 is included in the series, then which of the following will change?
I. Median II. Mode III. Standard deviation
A. I only B. II only C. III only D. I and III only E. I, II and III Mode will not change, earlier it was 15, now also it'll be 15. Mode= Element that occurs maximum number of times(Frequency). Median will change, earlier it was 15.5, now 15 Old list 10, 11, 12, 15, 15, 15, 17, 19, 20, 20 new list 10, 11, 12, 15, 15, 15, 15, 17, 19, 20, 20 VeritasKarishma EgmatQuantExpert could you help me how to quickly find whether there has been change in sd or not? EDIT: Median won't change, new median= 15, old median (15+15)/2=15.
_________________
Kindly drop a '+1 Kudos' if you find this post helpful.GMAT Math Book I never wanted what I gave up I never gave up what I wanted
Originally posted by LeoN88 on 22 May 2019, 23:59.
Last edited by LeoN88 on 23 May 2019, 01:50, edited 1 time in total.



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2943

Re: Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a
[#permalink]
Show Tags
23 May 2019, 00:33
LeoN88 wrote: Mode will not change, earlier it was 15, now also it'll be 15. Mode= Element that occurs maximum number of times(Frequency). Median will change, earlier it was 15.5, now 15 Old list 10, 11, 12, 15, 15, 15, 17, 19, 20, 20 new list 10, 11, 12, 15, 15, 15, 15, 17, 19, 20, 20 VeritasKarishma EgmatQuantExpert could you help me how to quickly find whether there has been change in sd or not? Hey LeoN88, The value of standard deviation will change slightly, as the mean changes slightly. If the mean of the original series was 15, then there would have been no change.
_________________



Intern
Joined: 27 Jun 2015
Posts: 45

Re: Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a
[#permalink]
Show Tags
23 May 2019, 01:03
LeoN88 wrote: Bunuel wrote: Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a number 15 is included in the series, then which of the following will change?
I. Median II. Mode III. Standard deviation
A. I only B. II only C. III only D. I and III only E. I, II and III Mode will not change, earlier it was 15, now also it'll be 15. Mode= Element that occurs maximum number of times(Frequency). Median will change, earlier it was 15.5, now 15 Old list 10, 11, 12, 15, 15, 15, 17, 19, 20, 20 new list 10, 11, 12, 15, 15, 15, 15, 17, 19, 20, 20 VeritasKarishma EgmatQuantExpert could you help me how to quickly find whether there has been change in sd or not? Hi, Median wil not change as for old series also median is equal to 15. For even number terms we take the avg of values ( 15+15)/2 Posted from my mobile device



ISB School Moderator
Joined: 08 Dec 2013
Posts: 530
Location: India
Concentration: Nonprofit, Sustainability
WE: Operations (NonProfit and Government)

Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a
[#permalink]
Show Tags
23 May 2019, 01:32
vishumangal wrote: LeoN88 wrote: Bunuel wrote: Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a number 15 is included in the series, then which of the following will change?
I. Median II. Mode III. Standard deviation
A. I only B. II only C. III only D. I and III only E. I, II and III Mode will not change, earlier it was 15, now also it'll be 15. Mode= Element that occurs maximum number of times(Frequency). Median will change, earlier it was 15.5, now 15 Old list 10, 11, 12, 15, 15, 15, 17, 19, 20, 20 new list 10, 11, 12, 15, 15, 15, 15, 17, 19, 20, 20 VeritasKarishma EgmatQuantExpert could you help me how to quickly find whether there has been change in sd or not? Hi, Median wil not change as for old series also median is equal to 15. For even number terms we take the avg of values ( 15+15)/2 Posted from my mobile deviceCould you check once again. old list has 15 and 15 in the middle so, median= mean of middlemost elements= 15.5 New list has 15 in the middle so median is 15.
_________________
Kindly drop a '+1 Kudos' if you find this post helpful.GMAT Math Book I never wanted what I gave up I never gave up what I wanted



Intern
Joined: 27 Jun 2015
Posts: 45

Re: Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a
[#permalink]
Show Tags
23 May 2019, 01:45
Hi,if sum 15 +15 it comes out to be 30 and when you divide it by 2 that is 30/2 = 15
Posted from my mobile device



ISB School Moderator
Joined: 08 Dec 2013
Posts: 530
Location: India
Concentration: Nonprofit, Sustainability
WE: Operations (NonProfit and Government)

Re: Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a
[#permalink]
Show Tags
23 May 2019, 01:47
vishumangal wrote: Hi,if sum 15 +15 it comes out to be 30 and when you divide it by 2 that is 30/2 = 15
Posted from my mobile device Sorry, silly mistake mean of 15 and 15 is 15. You're right.
_________________
Kindly drop a '+1 Kudos' if you find this post helpful.GMAT Math Book I never wanted what I gave up I never gave up what I wanted



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9446
Location: Pune, India

Re: Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a
[#permalink]
Show Tags
23 May 2019, 08:58
LeoN88 wrote: Bunuel wrote: Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a number 15 is included in the series, then which of the following will change?
I. Median II. Mode III. Standard deviation
A. I only B. II only C. III only D. I and III only E. I, II and III Mode will not change, earlier it was 15, now also it'll be 15. Mode= Element that occurs maximum number of times(Frequency). Median will change, earlier it was 15.5, now 15 Old list 10, 11, 12, 15, 15, 15, 17, 19, 20, 20 new list 10, 11, 12, 15, 15, 15, 15, 17, 19, 20, 20 VeritasKarishma EgmatQuantExpert could you help me how to quickly find whether there has been change in sd or not? EDIT: Median won't change, new median= 15, old median (15+15)/2=15. In this question, I know that median and mode won't change. They were both 15 before and continue to be the same. So obviously, looking at the options, SD must change. There is no option that says none of the 3 quantities will change. Answer must be (C). That said, a trickier version of the question might need you to evaluate the change in SD. {10, 11, 12, 15, 15, 15, 17, 19, 20, 20} Note here that mean will be a bit more than 15. (since shortfall is 12 while extra is 16 assuming 15 to be the mean) When you add another 15 to it, the numerator will increase by a small quantity while the denominator will increase by 1. The SD will decrease slightly. You know this because when you add the same number to numerator and denominator of a number greater than 1, the number decreases and goes toward 1. If you want to keep the number same you need to add 'a' to numerator and 'b' denominator such that a is greater than b. For more on this, check: https://www.veritasprep.com/blog/2011/0 ... roundone/Another point, if the initial list's mean were 15, adding 15 to it would have certainly reduced the SD since numerator would not have changed while the denominator would have increased by 1. Check here: https://www.veritasprep.com//blog/2012/ ... deviation/https://www.veritasprep.com/blog/2016/0 ... mulagmat/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4252
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a
[#permalink]
Show Tags
23 May 2019, 09:43
Bunuel wrote: Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a number 15 is included in the series, then which of the following will change?
I. Median II. Mode III. Standard deviation
A. I only B. II only C. III only D. I and III only E. I, II and III inclusion of 15 in the set will not change the median and mode but for SD ; i,e the variation of value along the mean will vary as we will have 1 more additional entry of the value ... IMO C
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.



CrackVerbal Quant Expert
Joined: 12 Apr 2019
Posts: 178

Re: Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a
[#permalink]
Show Tags
04 Jun 2019, 08:19
This question is a moderately difficult question on Statistics. It tests your understanding of the statistical measures. The median is the middle value (when there are an odd number of values), when all the values in the data set are arranged in ascending order/descending order. In case there are even number of values in the set, the median is the average of the two values in the middle. The mode is that value that is seen most frequently in the data set. Standard deviation is the root of the mean of the squared deviations, calculated with reference to the mean. In this question, since there are 10 values, the median will be the average of the 5th and the 6th values. Since both these values are 15, the median = 15. When one more 15 is included in the set, the number of values in the set becomes 11 and the median becomes the 6th value. But the 6th value IS 15. Therefore, the median does not change. So, statement I should not be a part of the answer. Options A, D and E can be eliminated basis this. In the set of values given, the number 15 occurs thrice and hence is the mode. When we introduce one more 15, the mode will still remain 15. Therefore, statement II is also not a part of the answer. Option B can be eliminated. The correct answer option should be C. The mean of the given set of values is \(\frac{154}{10}\) = 15.4. When another 15 is added, the mean reduces to \(\frac{169}{11}\) = 15.3. Because of this, the standard deviation is bound to change. Therefore, statement III only has to be the answer. Remember that, the Standard deviation of a set of values always depends on the mean. You change things in a way it affects the mean, the standard deviation also gets affected. On the timing front, this is a question which can be solved in about 1 minute. Hope this helps!
_________________




Re: Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a
[#permalink]
04 Jun 2019, 08:19






