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What is the median of the observations 4,5,7,x,2 ?

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by vinni.k » Tue May 29, 2012 8:04 am
What is the median of the observations 4,5,7,x,2 ?

(1). The average of the given observations is 4
(2). The mode of the given observations is 3

Answer is D

Hi All,

The above one is from prep company. So far in GMAT, i haven't encountered any question of statistics that mentions "mode." I am not sure whether this type "mode" is asked or not. However, if it is, then i don't know how to solve for mode. Please help on this one.
The (1) is simple and easy to get the value of x. (2) is out of my reach.

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Vinni
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by mathewmithun » Tue May 29, 2012 9:10 am
vinni.k wrote:What is the median of the observations 4,5,7,x,2 ?

(1). The average of the given observations is 4
(2). The mode of the given observations is 3

Answer is D

Hi All,

The above one is from prep company. So far in GMAT, i haven't encountered any question of statistics that mentions "mode." I am not sure whether this type "mode" is asked or not. However, if it is, then i don't know how to solve for mode. Please help on this one.
The (1) is simple and easy to get the value of x. (2) is out of my reach.

Thanks & Regards
Vinni
Will try my best:

Statement 1 is simple and is sufficient to answer

Statement 2: Mode means number or numbers that appear most frequently. Since the question says 3 and from the given set 3 can appear at max once (when x=3), mode cannot be 3. In fact when x is not equal to 4,5,7,2 we have no mode. so statement 2 is contradictory according to me and So I will stick with A.
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by vinni.k » Tue May 29, 2012 10:27 am
mathewmithun wrote:
Will try my best:

Statement 1 is simple and is sufficient to answer

Statement 2: Mode means number or numbers that appear most frequently. Since the question says 3 and from the given set 3 can appear at max once (when x=3), mode cannot be 3. In fact when x is not equal to 4,5,7,2 we have no mode. so statement 2 is contradictory according to me and So I will stick with A.
Nope, answer is D. Mode is confusing me.
Can anyone please explain this mode in detail ? and Does GMAT ask questions based on mode ?

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by Brent@GMATPrepNow » Tue May 29, 2012 10:38 am
vinni.k wrote: Nope, answer is D. Mode is confusing me.
Can anyone please explain this mode in detail ? and Does GMAT ask questions based on mode ?
vinni
From the OG13:

The mode of a list of numbers is the number that occurs most frequently in the list.
For example, the mode of 1, 3, 6, 4, 3, 5 is 3.

A list of numbers may have more than one mode.
For example, the list 1, 2, 3, 3, 3, 5, 7, 10, 10, 10, 20 has two modes, 3 and 10.

As you can see, there is no value for x that will give us a mode of 3 for the numbers 4,5,7,x,2

Are you sure you wrote the question correctly? What's the source?

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Brent
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by Brent@GMATPrepNow » Tue May 29, 2012 10:38 am
I have a feeling that statement 2 is supposed to read:

(2) The mode of the given observations is 2

In this case, the answer to the question would be D

Cheers,
Brent
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by vinni.k » Tue May 29, 2012 12:22 pm
Brent@GMATPrepNow wrote:I have a feeling that statement 2 is supposed to read:

(2) The mode of the given observations is 2

In this case, the answer to the question would be D

Cheers,
Brent
Brent, thanks for your reply.

The source is "IMS max-prep"

I have checked the statement (2) again, and it is correct. The mode of the given observations is 3.

and the explanation given for statement (2) is - We know that the mode is 3 and hence to make the mode of the observations 3, x has to be equal to 3. Hence, this is also enough.

I am not sure what does this mean :?

Thanks
Vinni
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