Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49860

In a set of data, the average (arithmetic mean) equals the median. Whi
[#permalink]
Show Tags
06 Jun 2017, 11:29
Question Stats:
47% (00:45) correct 53% (00:36) wrong based on 100 sessions
HideShow timer Statistics



Manager
Joined: 24 Dec 2016
Posts: 92
Location: India
Concentration: Finance, General Management
WE: Information Technology (Computer Software)

In a set of data, the average (arithmetic mean) equals the median. Whi
[#permalink]
Show Tags
06 Jun 2017, 22:55
Bunuel wrote: In a set of data, the average (arithmetic mean) equals the median. Which of the following must be true?
I. The set consists of evenly spaced numbers. II. The set consists of an odd number of terms. III. The set has no mode.
A. I only B. I and II C. II and III D. I, II, and III E. None of the above Per question, AM=Median. Lets take a look at a few sets where the relation is true. A {2,4,6,8}  Here AM= Median and the set is equally spaced B {10, 12, 14.5, 16, 20}  Here also AM=Median= 14.5 but the set isn't equally spaced. C {11, 19, 19, 27}  Here also AM = Median = 19 but the set isnt equally spaced. Now, lets check the options. I is incorrect, by sets B and C II is incorrect by set A and C III is incorrect by set C. Answer should be E.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8374
Location: Pune, India

Re: In a set of data, the average (arithmetic mean) equals the median. Whi
[#permalink]
Show Tags
07 Jun 2017, 02:52
Bunuel wrote: In a set of data, the average (arithmetic mean) equals the median. Which of the following must be true?
I. The set consists of evenly spaced numbers. II. The set consists of an odd number of terms. III. The set has no mode.
A. I only B. I and II C. II and III D. I, II, and III E. None of the above We need to find whether the following 'must be true': I. The set consists of evenly spaced numbers. Is it necessary? Can we not have a set in which mean = median but the set is not evenly spaced? Such as 1, 4, 4, 5, 6 Here mean = median = 4, but the set is not evenly spaced. So this condition is not necessary. II. The set consists of an odd number of terms. Is this condition necessary? 3, 4, 4, 5 has an even number of terms but mean = median = 4. So this condition is also not necessary. III. The set has no mode. The example above 3, 4, 4, 5 has a mode but mean = median = 4. So this condition is also not necessary. Answer (E)
_________________
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 selfstudy has never been more personalized or more fun. Try ORION Free!



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8374
Location: Pune, India

Re: In a set of data, the average (arithmetic mean) equals the median. Whi
[#permalink]
Show Tags
10 Jun 2017, 06:43
VeritasPrepKarishma wrote: Bunuel wrote: In a set of data, the average (arithmetic mean) equals the median. Which of the following must be true?
I. The set consists of evenly spaced numbers. II. The set consists of an odd number of terms. III. The set has no mode.
A. I only B. I and II C. II and III D. I, II, and III E. None of the above We need to find whether the following 'must be true': I. The set consists of evenly spaced numbers. Is it necessary? Can we not have a set in which mean = median but the set is not evenly spaced? Such as 1, 4, 4, 5, 6 Here mean = median = 4, but the set is not evenly spaced. So this condition is not necessary. II. The set consists of an odd number of terms. Is this condition necessary? 3, 4, 4, 5 has an even number of terms but mean = median = 4. So this condition is also not necessary. III. The set has no mode. The example above 3, 4, 4, 5 has a mode but mean = median = 4. So this condition is also not necessary. Answer (E) Responding to a pm: Quote: Just to confirm, I think logic in this question is inversely true. Meaning, if a set contains evenly spaced numbers, and have odd number of terms then the mean and median are same. is this always right?
In an evenly spaced set, mean will be equal to median. It doesn't matter whether the number of elements is even or odd. 1, 3, 5 Mean = median = 3 1, 3, 5, 7 Mean = median = 4
_________________
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 selfstudy has never been more personalized or more fun. Try ORION Free!



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: In a set of data, the average (arithmetic mean) equals the median. Whi
[#permalink]
Show Tags
10 Jun 2017, 07:20
Bunuel wrote: In a set of data, the average (arithmetic mean) equals the median. Which of the following must be true?
I. The set consists of evenly spaced numbers. II. The set consists of an odd number of terms. III. The set has no mode.
A. I only B. I and II C. II and III D. I, II, and III E. None of the above Let’s analyze each Roman numeral with examples to determine whether it must be true. I. The set consists of evenly spaced numbers. This does not have to be true. For example, let’s say the set consists of the following numbers: 1, 2, 4, 6, 7. The mean and median are both 4, but this is not a set of evenly spaced numbers (notice that 2 is one more than 1, but 4 is two more than 2). II. The set consists of an odd number of terms. This does not have to be true. For example, let’s say the set consists of the following numbers: 1, 1. The mean and median are both 1, but this set has 2 terms. III. The set has no mode. This does not have to be true. For example, let’s say the set consists of the following numbers: 1, 2, 2, 3. The mean and median are both 2, which is also the mode of the set. Answer: E
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



NonHuman User
Joined: 09 Sep 2013
Posts: 8404

Re: In a set of data, the average (arithmetic mean) equals the median. Whi
[#permalink]
Show Tags
30 Sep 2018, 06:35
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: In a set of data, the average (arithmetic mean) equals the median. Whi &nbs
[#permalink]
30 Sep 2018, 06:35






