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Is the median equal to 10

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Is the median equal to 10

by hardik.jadeja » Mon Feb 09, 2009 1:43 pm
The arithmetic mean (average) of a set of 10 numbers is 10. Is the median value of the same set also equal to 10?

1. Exactly half of the numbers are less than 10.
2. The mode of the set of numbers is 10.

OA is E
IMO it should be C

My Logic:
Clearly 1 and 2 alone are insufficient. So A,B and D are ruled out. But when 1 & 2 are taken together..

We know we have 5 numbers in the set that are less than 10. (given in statement 1). Other 5 numbers can be 10(not all 5) or more than 10.
And we also know that 10 occurs more than once in the set as 10 is the mode of the set.

So when we arrange these numbers in ascending order we will have a number less than 10 at the fifth place and 10 at the 6th place. This is enough to figure out that median will not be 10 because the average of the 2 middle numbers(5th & 6th) will not be 10.

Correct me if I am wrong?
Last edited by hardik.jadeja on Mon Feb 09, 2009 11:55 pm, edited 1 time in total.
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by mrsmarthi » Mon Feb 09, 2009 5:03 pm
IMO B.

There is an emperical forumla

Mode = 3 Median - 2 Mean.

So if we know atleast 2 of the values, we can know the other one.

From question stem we know that mean = 10.

From stmt 2, Mode = 10.

Using the emperical formula, we can calcuate Median, and there by decide if it is equal to Mean or not.

From stmt1, we canot say whether Median is equal to 10 or not. Insufficient.
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by hardik.jadeja » Mon Feb 09, 2009 10:36 pm
Hi mrsmarthi,

The equation median ≈ (2 × mean + mode)/3 only gives you approximate value of median. It only applies to slightly non-symmetric distributions that resemble a normal distribution.

However, this equation is not always true and the three statistics(Mean, Median and Mode) can appear in any order. Specially when we have much larger standard deviation and the distribution is strongly skewed.

That's why I don't think B is the right answer. Correct me if I am wrong.
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Re: Is the median equal to 10

by x2suresh » Mon Feb 09, 2009 10:59 pm
hardik.jadeja wrote:The arithmetic mean (average) of a set of 10 numbers is 10. Is the median value of the same set also equal to 10?

1. Exactly half of the numbers are less than 10.
2. The mode of the set of numbers is 10.

OA is E
IMO it should be C

My Logic:
Clearly 1 and 2 alone are insufficient. So A,B and D are ruled out. But when 1 & 2 are taken together..

We know we have 5 numbers in the set that are less than 10. (given in statement 1). Other 5 numbers can be 10(not all 5) or more than 10.
And we also know that 10 occurs more than once in the set as 10 is the mode of the set.

So when we arrange these numbers in ascending order we will have a number less than 10 on the fifth place and 10 on the 6th place. This is enough to figure out that median will not be 10 because the average of the 2 middle numbers(5th & 6th) will not be 10.

Correct me if I am wrong?

Agree with your logic. when combined median <>10

It should be C

what is the source.
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by ontopofit » Tue Feb 10, 2009 12:56 pm
it's E.

so here evryone agrees that it cud not be solved with either 1) or 2).

with C I will give one series.

1,2,3,4,5,6,7,10,10,52.

mode =10, mean =10, but median = 5.5.
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by x2suresh » Tue Feb 10, 2009 1:14 pm
ontopofit wrote:it's E.

so here evryone agrees that it cud not be solved with either 1) or 2).

with C I will give one series.

1,2,3,4,5,6,7,10,10,52.

mode =10, mean =10, but median = 5.5.

Question: Is the median value of the same set also equal to 10?
Answer is NO.

because median <>10 thats what your example shows.

Can you show another example where median =10..
thats not possible.


So C should be the answer.
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by mjjking » Thu Feb 12, 2009 6:59 am
exactly, a NO answer is a correct answer nonetheless.
so C
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by avenus » Thu Feb 12, 2009 3:52 pm
x2suresh, the example you were asking for:

{6 7 8 9 10 10 11 12 13 14}

Mean = 10
Median = 10
Mode = 10
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by x2suresh » Thu Feb 12, 2009 7:51 pm
avenus wrote:x2suresh, the example you were asking for:

{6 7 8 9 10 10 11 12 13 14}

Mean = 10
Median = 10
Mode = 10
This voilates first statment.. only 4 numbers (i.e <half of numbers) are less than 10


1. Exactly half of the numbers are less than 10.


It should be C.
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by kris_hansy » Sun Mar 01, 2009 9:13 am
Isn't there something that says:

Mean < Median < Mode
OR
Mean > Median > Mode
OR
Mean <=Median<=Mode
OR
Mean=>Median=>Mode

So, by this since Mean = Mode, hence Mean = Median = Mode
(Median should always fall between the two)
Hence, (B)

Am I wrong?
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