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## mean, median and mode

This topic has 2 expert replies and 12 member replies
ch0719 Senior | Next Rank: 100 Posts
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#### mean, median and mode

Wed Dec 24, 2008 2:37 pm
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
The mode of a set of integers is x. What is the difference between the median of this set of integers and x?
1. The difference between any two integers in the set is less than 3
2. The average of the set of integers is x

It kind of make sense after I have tried out several sets of numbers, but still puzzled at how to reach a conclusion on this in a limited time range

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cramya Legendary Member
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Wed Dec 24, 2008 4:37 pm
These conceptual statistics questions are always a headache....

Stmt I - ws able to eliminate it easily

1 2 3 3

mode=3 median2.5 difference - .5

0 1 2 2 3

mode = 2 median - 2 difference -0

INSUFF

Stmt II

I was thinking if the mode is x and the average (middle value is x) then the median has to be x. I was not able to come up with a set of numbers where the mode is x, average is x but the median is not x.
I was thinking B) when I did this problem.

I will also patiently wait for a better technique

Ch,
How did u prove stmt II was INSUFFICIENT?

logitech Legendary Member
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Wed Dec 24, 2008 8:01 pm
ch0719 wrote:
The mode of a set of integers is x. What is the difference between the median of this set of integers and x?
1. The difference between any two integers in the set is less than 3
2. The average of the set of integers is x

It kind of make sense after I have tried out several sets of numbers, but still puzzled at how to reach a conclusion on this in a limited time range
Let's refresh our memories first:

Definition: The mode of a set of data is the value in the set that occurs most often.

ST1) means range of the set is < 3 we have no other data. INSUF
ST2) The average of the set of integers is value in the set that occurs most often.

AV - MOD(AV) AV +

This means that the both ends of the set have same distance to the average

1 2 2 2 3

The mean is 2 , the average is 2 and mode 2

-9 1 1 11 the mean is 1, the average is 1 and mode 1

So I don't know why the answer is not B.

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ch0719 Senior | Next Rank: 100 Posts
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Wed Dec 24, 2008 10:10 pm
considering the set {1,3,6,10,10,30}

ave = mode = 10
but median is 8

I have tried several sets and this is one that made st2 insf.

what I did was to assume a and b two integers lower than 10 in the set below:

{a,b,6,10,10,30} and in this set, 10 is the mode since a does not equal to b

now st2 told us that ave=mode therefore in this case = 10

so [(a+b)+6+10+10+30]/6=10

we find (a+b)=4 so a could be 1 and b could be 3

and so in this case, the median is (6+10)/2 which is 8

ST2 Insf

cramya Legendary Member
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Wed Dec 24, 2008 10:22 pm
Thanks! Seriously how long did it take for you to come up with this set?

God help us for problems like these . IMO finding a set to prove a statement's insufficieny wihtin 2 minutes or say max 3 is the hardest part.

Whats the source? Do they have any explanation on stmt I and II's( together) sufficiency or is it just by picking numbers?

ch0719 Senior | Next Rank: 100 Posts
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Wed Dec 24, 2008 10:35 pm
No it does not offer any official explanations

I think that it is still possible to eliminate A & B within 2 min, and if u r just so good at statistics may be able to pick C as the right choice, otherwise w may have to use our best judgment on this kind of questions

I was thinking about skewness on St. 2, that if the set is very skewed the statement may not hold true, that's when I came with the example set above...

Last edited by ch0719 on Thu Dec 25, 2008 1:51 am; edited 1 time in total

amitabhprasad Master | Next Rank: 500 Posts
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Wed Dec 24, 2008 11:16 pm
ch0719,
A friendly advice. Don't post questions from actual GMAT, I believe it will have some adverse consequences

cramya Legendary Member
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Thu Dec 25, 2008 12:41 am
Quote:
A friendly advice. Don't post questions from actual GMAT, I believe it will have some adverse consequences
Agree!

Quote:
This question is from my friend, she got a ton of exercises from her Gmat prep in China, many of the questions were said from the actual test, wrote onto online forum by test takers
Ch,

Not sure what u meant here. Did u mean its a question from an gmat online prep company in China or actual GMAT? If its from the actual GMAT please request the moderators to remove the post.

Regards,
Cramya

ch0719 Senior | Next Rank: 100 Posts
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Thu Dec 25, 2008 2:16 am
The question I post is sent to me by a friend who got it from a gmat prep company in China, which I have heard that they might have used real gmat questions, but this is not for sure.

Just to be cautious and to not stir any controversial matter in this forum I have edited my reply regarding the source of the question.

nagesh.bvrch@gmail.com Newbie | Next Rank: 10 Posts
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Wed Sep 01, 2010 1:05 am
find the mode of the set of numbers {1,1,2,2,3,4,5}

singhsa Master | Next Rank: 500 Posts
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Tue Sep 07, 2010 3:54 pm
cramya wrote:
Thanks! Seriously how long did it take for you to come up with this set?

God help us for problems like these . IMO finding a set to prove a statement's insufficieny wihtin 2 minutes or say max 3 is the hardest part.

Whats the source? Do they have any explanation on stmt I and II's( together) sufficiency or is it just by picking numbers?
The answer should def be B here. And this can be solved within a minute.
The formula applied here is : Mode= 3 Mean -2 Median
Mode=x; mean=x, so
x=3x - 2mode
Therefore, Mode= x
Thus we can find out the difference.

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Stuart Kovinsky GMAT Instructor
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Wed Sep 08, 2010 10:31 am
singhsa wrote:
cramya wrote:
Thanks! Seriously how long did it take for you to come up with this set?

God help us for problems like these . IMO finding a set to prove a statement's insufficieny wihtin 2 minutes or say max 3 is the hardest part.

Whats the source? Do they have any explanation on stmt I and II's( together) sufficiency or is it just by picking numbers?
The answer should def be B here. And this can be solved within a minute.
The formula applied here is : Mode= 3 Mean -2 Median
Mode=x; mean=x, so
x=3x - 2mode
Therefore, Mode= x
Thus we can find out the difference.
Hi,

(2) is definitely not sufficient.

(2) simply tells us that the average = mode. Just because the average is the most frequently occurring term doesn't mean that the average = median.

For example, consider the set: {1, 10, 10, 12, 13, 14}

average = 60/6 = 10
mode = 10
median = (10 + 12)/2 = 11

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singhsa Master | Next Rank: 500 Posts
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Wed Sep 08, 2010 12:30 pm
Oh ya Stuart, this rule definitely does'nt hold out against the particular example you've considered.

So, is this formula even correct? I'v never seen this formula been applied in any of the forums. I thought this was the best possiblility for the application of this formula..... ...do we require this formula in the GMAT ??

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Ian Stewart GMAT Instructor
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Wed Sep 08, 2010 12:31 pm
singhsa wrote:
The answer should def be B here. And this can be solved within a minute.
The formula applied here is : Mode= 3 Mean -2 Median
There is no such formula, as you can see by taking pretty much any set at random. Try {0, 0, 1, 99}, for example; the mean is 25, the mode is 0 and the median is 0.5. That formula doesn't work.

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s_harsha Newbie | Next Rank: 10 Posts
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Fri Dec 09, 2011 8:06 pm
Hello Ian Stewart,

For this DS question, can we conclude that Fact statement 1 is insufficient, simply because there is no relation between median and mode and get along.

Also can we conclude that fact statement 2 is also insufficient because there is no relation between mean, mode and median as we do not know if the set is consecutive.

My basic question on all these mean, mode and median problems on GMAT is that, can a student conclude the statement to be In sufficient if he/she cannot prove that the set is consecutive?

Regards,

Harsha

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