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# The median value of a set of 9 positive integers is 6. If

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Manager
Joined: 24 Jan 2005
Posts: 209
Location: Boston
The median value of a set of 9 positive integers is 6. If  [#permalink]

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24 Feb 2005, 17:27
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Question Stats:

33% (01:17) correct 67% (01:37) wrong based on 18 sessions

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The median value of a set of 9 positive integers is 6. If the only mode in the distrubution is 25 what is the least possible mean of the distribution.

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VP
Joined: 18 Nov 2004
Posts: 1374

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Updated on: 24 Feb 2005, 18:19
9

numbers shud be....1,2,3,4,6,7,8,25,25 = 81/9 = 9

Originally posted by banerjeea_98 on 24 Feb 2005, 17:40.
Last edited by banerjeea_98 on 24 Feb 2005, 18:19, edited 1 time in total.
VP
Joined: 18 Nov 2004
Posts: 1374

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24 Feb 2005, 18:19
MA wrote:
banerjeea_98 wrote:
9

numbers shud be....1,2,3,4,5,6,7,8,25,25 = 81/9 = 9

baner, 5 cannot be in the series.

sorry that was a typo....ans remains the same
Manager
Joined: 01 Jan 2005
Posts: 159
Location: NJ

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25 Feb 2005, 03:31
Hmm... In the beginning I couldn't und the q at all but after seeing banerjee's post, I think he is right.
Intern
Joined: 09 Jan 2005
Posts: 20

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25 Feb 2005, 05:01
2,3,4,5,6,25,25,25,25 ;

Even this could be a plausible series. Mode can be repeated any number of times.

There is a formula which relates mean, median and mode -
3 * mean - 2 * mode = median

The answer is 17 ( minimum possible value of the mean)
VP
Joined: 18 Nov 2004
Posts: 1374

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25 Feb 2005, 06:21
HSWKM wrote:
2,3,4,5,6,25,25,25,25 ;

Even this could be a plausible series. Mode can be repeated any number of times.

There is a formula which relates mean, median and mode -
3 * mean - 2 * mode = median

The answer is 17 ( minimum possible value of the mean)

Stem asks for the least possible mean, therefore, we need to keep 25s to the minimum.
Manager
Joined: 18 Nov 2004
Posts: 72

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25 Feb 2005, 07:52
i get 9 as well

1+2+3+4+6+7+8+25+25=81
81/9=9
Manager
Joined: 25 Oct 2004
Posts: 235

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25 Feb 2005, 10:50
The series is 1,2,3,4,6,7,8,25,25
So the mean is 81/9=9
Manager
Joined: 08 Oct 2004
Posts: 223

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28 Feb 2005, 22:00
MA wrote:
banerjeea_98 wrote:
9

numbers shud be....1,2,3,4,5,6,7,8,25,25 = 81/9 = 9

baner, 5 cannot be in the series.

Please could you explain why 5 cannot be a part of the series?

Thanks
_________________

Believe in yourself.

Manager
Joined: 27 Jan 2005
Posts: 97
Location: San Jose,USA- India

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28 Feb 2005, 22:39
1
Problem says mean should be least possible.So we should try to keep the numbers as small as possible.

6 is the median,middle number.So there are 4 numbers greater than 6 and 4 numbers less than 6.

Mode is 25 only.So one of the numbers is 25.But it is the only mode,so there should be one more 25 to make it "the only mode".

Still we donot know the 4 numbers less than 6 and the 2 numbers greater than 6.We need to keep the numbers as small as possible.So, the 4 numbers that are less than 6 can be 1,2,3,4 . cant go smaller than that.Similarly missing two numbers that are greater than 6 are 7,8 (smallest possible).

So numbers are 1,2,3,4,6,7,8,25,25.
phew....lengthy explanation.
Intern
Joined: 09 Jan 2005
Posts: 20

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01 Mar 2005, 02:32
Yep. Silly mistake that. Question is asking minimum value of mean. Answer is indeed 9. Thanks banerjee
Manager
Joined: 11 Jan 2005
Posts: 99

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01 Mar 2005, 03:23
one more for 9

first mode :
two 25

second the median : 6

we are left with : 6 postive integer to pick with the objective of making the mean the smallest

so we have to pick from both side of the median the smallest positive integers :

1, 2 , 3, 4
7,8, 25 , 25

mean 9
Director
Joined: 27 Dec 2004
Posts: 846

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01 Mar 2005, 09:47
700Plus wrote:
Problem says mean should be least possible.So we should try to keep the numbers as small as possible.

6 is the median,middle number.So there are 4 numbers greater than 6 and 4 numbers less than 6.

Mode is 25 only.So one of the numbers is 25.But it is the only mode,so there should be one more 25 to make it "the only mode".

Still we donot know the 4 numbers less than 6 and the 2 numbers greater than 6.We need to keep the numbers as small as possible.So, the 4 numbers that are less than 6 can be 1,2,3,4 . cant go smaller than that.Similarly missing two numbers that are greater than 6 are 7,8 (smallest possible).

So numbers are 1,2,3,4,6,7,8,25,25.
phew....lengthy explanation.

lengthy but clear. Thanks for taking time to break it down because now i do understand it.
Manager
Joined: 24 Jan 2005
Posts: 209
Location: Boston

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04 Mar 2005, 12:54
Yes that's a good and detailed explanation
Senior Manager
Joined: 02 Feb 2004
Posts: 336

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12 Mar 2005, 07:58
banerjeea_98 wrote:
9

numbers shud be....1,2,3,4,6,7,8,25,25 = 81/9 = 9

why it can't be numbers shud be...0,.1,2,3,,6,7,8,25,25. isn't zero an integer?
VP
Joined: 18 Nov 2004
Posts: 1374

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12 Mar 2005, 17:04
mirhaque wrote:
banerjeea_98 wrote:
9

numbers shud be....1,2,3,4,6,7,8,25,25 = 81/9 = 9

why it can't be numbers shud be...0,.1,2,3,,6,7,8,25,25. isn't zero an integer?

0 is not +ve or -ve, ques says +ve integers only
Manager
Affiliations: Beta Gamma Sigma
Joined: 14 Aug 2008
Posts: 196
Schools: Harvard, Penn, Maryland

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28 Dec 2009, 17:40
where does it say you can't repeat?

couldn't it be

1,1,1,1,6,6,6,25,25

for 72/9 = 8

What is the source?
Manager
Affiliations: Beta Gamma Sigma
Joined: 14 Aug 2008
Posts: 196
Schools: Harvard, Penn, Maryland

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28 Dec 2009, 17:42
oh mode is 25 nvrmnd
Manager
Joined: 30 Jun 2004
Posts: 145
Location: Singapore

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29 Dec 2009, 23:50
700Plus wrote:
Problem says mean should be least possible.So we should try to keep the numbers as small as possible.

6 is the median,middle number.So there are 4 numbers greater than 6 and 4 numbers less than 6.

Mode is 25 only.So one of the numbers is 25.But it is the only mode,so there should be one more 25 to make it "the only mode".

Still we donot know the 4 numbers less than 6 and the 2 numbers greater than 6.We need to keep the numbers as small as possible.So, the 4 numbers that are less than 6 can be 1,2,3,4 . cant go smaller than that.Similarly missing two numbers that are greater than 6 are 7,8 (smallest possible).

So numbers are 1,2,3,4,6,7,8,25,25.
phew....lengthy explanation.

Thanks for clear explanation.
Math Expert
Joined: 02 Sep 2009
Posts: 52161

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30 Dec 2009, 07:27
mirhaque wrote:
banerjeea_98 wrote:
9

numbers shud be....1,2,3,4,6,7,8,25,25 = 81/9 = 9

why it can't be numbers shud be...0,.1,2,3,,6,7,8,25,25. isn't zero an integer?

Sure it's an integer but not positive: "9 positive integers"

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This discussion does not meet community quality standards. It has been retired.

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Re: &nbs [#permalink] 30 Dec 2009, 07:27

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