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For a certain set of n numbers, where n > 1, is the average [#permalink]
11 Mar 2009, 17:24

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Difficulty:

65% (hard)

Question Stats:

52% (01:40) correct
48% (05:57) wrong based on 109 sessions

For a certain set of n numbers, where n > 1, is the average (arithmetic mean) equal to the median?

(1) If the n numbers in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2. (2) The range of n numbers in the set is 2(n - 1).

Re: For a certain set of n numbers, where n > 1, is the [#permalink]
05 Oct 2013, 06:08

Hello Can someone please help me in finding my mistake.

Given: The range is 2(n-1)

Now we know that:

last term = first term +(n-1)d

last term - first term = range = (n-1)d

Comparing we get d = 2

This means that the sequence is AP.

However, going by number putting techinque, I can see that the above result is not necessary true. Can someone please explain my mistake. _________________

Re: For a certain set of n numbers, where n > 1, is the average [#permalink]
15 May 2014, 10:50

ugimba wrote:

For a certain set of n numbers, where n > 1, is the average (arithmetic mean) equal to the median?

(1) If the n numbers in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2. (2) The range of n numbers in the set is 2(n - 1).

I thought that 2(n-1) was the range for both n consecutive even/odd integers Therefore, we still have an evenly spaced set Thus, 2 was sufficient

Could someone please advice where am I going wrong here?

Re: For a certain set of n numbers, where n > 1, is the average [#permalink]
16 May 2014, 01:26

1

This post received KUDOS

Expert's post

jlgdr wrote:

ugimba wrote:

For a certain set of n numbers, where n > 1, is the average (arithmetic mean) equal to the median?

(1) If the n numbers in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2. (2) The range of n numbers in the set is 2(n - 1).

I thought that 2(n-1) was the range for both n consecutive even/odd integers Therefore, we still have an evenly spaced set Thus, 2 was sufficient

Could someone please advice where am I going wrong here?

Thanks! Cheers J

But the reverse is not necessarily true: not all n-element sets which have the range equal to 2(n - 1) are consecutive odd or consecutive even integers.

For example, {2, 3, 6} has the range equal to 2(n - 1) but this set is not of that type. _________________

Re: For a certain set of n numbers, where n > 1, is the average [#permalink]
16 May 2014, 01:27

Expert's post

1

This post was BOOKMARKED

For a certain set of n numbers, where n > 1, is the average (arithmetic mean) equal to the median?

(1) If the n numbers in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2. This implies that the set is even;y spaced. In any evenly spaced set the mean (average) is equal to the median. Sufficient.

(2) The range of the n numbers in the set is 2(n- 1). This is completely useless. Not sufficient.

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