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Question about Evenly spaced set

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Question about Evenly spaced set

by RadiumBall » Wed Mar 23, 2011 8:44 pm
I saw these rules for Evenly spaced set in the MGMAT guide be it for even number of items or odd number of items
1) Mean and Median are the equal and is average of first and last term.
2) Sum of all elements is multiple of number of items.

I was wondering why does rule not apply to set such this {1, 2, 3, 4, 5 } ?
I thought even this is a evenly spaced set with even difference of 1.

Thanks
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by srcc25anu » Wed Mar 23, 2011 8:55 pm
for set {1,2,3,4,5}, N=5 (odd)
mean of {1,2,3,4,5} = sum of 5 terms / 5 or 15/5 = 3 Also we can say avg of 1 and 5 (avg of 1st and last terms) = 3
median = 3 (always will be the term in the middle (3rd term in this case) or avg of 1st and last terms (1+5/2) as opposed to when we have an even no. of itmes in the set - there will be no one middle term. Instead, the middle term will be the avg of 2 middle terms)
hence this illustrates the first point

sum of all elements = No. of terms * avg of 1st and last terms
= 5 * [(1+5)/2]
=5*3 = 15
And every number is a multiple of 1 so is 15. there isnt any apparent cotradiction.

Hope this is clear.
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by RadiumBall » Wed Mar 23, 2011 9:03 pm
No sorry I am not clear yet.

So let me ask with some examples why do the rules work for this set {4, 8, 12, 16, 20, 24 } and not for this set {1, 2, 3, 4, 5, 6 }?

Thanks.
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by srcc25anu » Wed Mar 23, 2011 9:11 pm
2) Sum of all elements is multiple of number of items.

I was wondering why does rule not apply to set such this {1, 2, 3, 4, 5 } ?

Sum of all elements in this set = 15 which is a multiple of 5 (no of items in the set)
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by srcc25anu » Wed Mar 23, 2011 9:18 pm
To my understanding, there can be 3 cases:

1. when n=odd and we have a clearly identifiable middle term, sum of terms is ALWAYS a multiple of n

2. if n=even, and all the terms are even in the set, then also Sum of terms is ALWAYS a multiple of n

3. BUT if n=even and all terms in the set are mix of odd and even numbers, then this is not true. sum of terms is not a multiple of n.
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by RadiumBall » Thu Mar 24, 2011 9:31 am
I am still clear on this...could anyone kindly clear this for me...
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by GMATGuruNY » Sun Mar 27, 2011 1:17 pm
RadiumBall wrote:I saw these rules for Evenly spaced set in the MGMAT guide be it for even number of items or odd number of items
1) Mean and Median are the equal and is average of first and last term.
2) Sum of all elements is multiple of number of items.

I was wondering why does rule not apply to set such this {1, 2, 3, 4, 5 } ?
I thought even this is a evenly spaced set with even difference of 1.

Thanks
I received a PM asking me to comment. The rules stated above are correct.

Given a set of evenly spaced values:

1) Average = median.
2) Average = (biggest + smallest)/2.
3) Number of values = (biggest - smallest)/(distance between each successive pair) + 1.
3) Sum = number of values * average

Thus, the sum is a multiple of the number of values in the set.

The set {1,2,3,4,5} adheres to all the rules listed above:

Average = (1+2+3+4+5)/5 = 3. Median = 3. Thus, average = median.
Average = (biggest + smallest)/2 = (5+1)/2 = 3. Same answer as above.
Number of values = (biggest - smallest)/(distance between each successive pair) + 1 = (5-1)/1 + 1 = 5.
Sum = number of values * average = 5*3 = 15.
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