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31 Jan 2012, 09:31
Kudos
Bookmarks
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 the N numbers in the set is 2(N-1).
The answer is A. I know 2 is insufficient. My understanding of the statement A is as difference is 2 they are consecutive even nos so irrespective of whether N is odd or even and N>1 (for N=10 or 11 ) the average alwalys equals the median for consecutive even nos.
Is my understanding correct ? Could someone confirm ? The actual explanation given in the book for statement 1 is bit confusing. That's why I want someone to confirm.
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 the N numbers in the set is 2(N-1).
The answer is A. I know 2 is insufficient. My understanding of the statement A is as difference is 2 they are consecutive even nos so irrespective of whether N is odd or even and N>1 (for N=10 or 11 ) the average alwalys equals the median for consecutive even nos.
Is my understanding correct ? Could someone confirm ? The actual explanation given in the book for statement 1 is bit confusing. That's why I want someone to confirm.
31 Jan 2012, 15:03
Kudos
Bookmarks
Hi, there. I'm happy to talk a little about this. 
You're perfectly right about Statement #2 -- it's not only insufficient --- it's completely useless.
Statement #1 says that the numbers are evenly-spaced, separated by steps of length 2.
They could be all evens: 6, 8, 10, 12, 14, . . . .
Or, they could be all odds: 5, 7, 9, 11, 13, . . . .
And actually, it doesn't matter. Here's a really easy rule-of-thumb to remember: on any list where all the numbers are even-spaced, the mean equals the median. Period. Starting point doesn't matter. Size of the space between the numbers doesn't matter. Even-spacing ---> mean = median.
The reason is: the mean always equals the median when the data is symmetric, and when each step is identical, then the whole set has mirror symmetry (imagine them as evenly-spaced dots on a number line).
Does that make sense? If you have any further question, please do no hesitate to ask.
Mike
You're perfectly right about Statement #2 -- it's not only insufficient --- it's completely useless.
Statement #1 says that the numbers are evenly-spaced, separated by steps of length 2.
They could be all evens: 6, 8, 10, 12, 14, . . . .
Or, they could be all odds: 5, 7, 9, 11, 13, . . . .
And actually, it doesn't matter. Here's a really easy rule-of-thumb to remember: on any list where all the numbers are even-spaced, the mean equals the median. Period. Starting point doesn't matter. Size of the space between the numbers doesn't matter. Even-spacing ---> mean = median.
The reason is: the mean always equals the median when the data is symmetric, and when each step is identical, then the whole set has mirror symmetry (imagine them as evenly-spaced dots on a number line).
Does that make sense? If you have any further question, please do no hesitate to ask.
Mike
