If the mean equals the median

Question

Hello,

Had a quick quant question... in questions were it is stated that in a set of numbers the mean equals the median. Does this mean that the set must be made up of consecutive numbers or numbers that are equally spaced or does only the reverse apply... ie. if we have a set of consecutive numbers or equally spaced numbers then the median equals the mean?

Thanks!

egmat · Answer

Hi there,

I wont give you the answer but a framework to answer this (because that matters in the end)

Case 1: mean == median; Can this be achieved in a set of non-consecutive/non evenly spaced numbers. Think of a case. 
Case 2: set of consecutive (or evenly spaced) numbers, does this mean that the mean is always equal to median

Let me know what you get.

-Rajat

alex1233 · Answer

Thanks a lot for the quick reply Rajat!

In order for case 1 to be true the numbers must be consecutive or evenly spaced
and likewise case 2 holds ie consecutive numbers (or evenly spaced sets) will always have a mean + to the median.

Please let me know if this reasoning is correct

thanks again for the quick reply!
Alex

egmat · Answer

Does case 1 require numbers to be consecutive or evenly spaced... how about:

0 4 8 11 17
0 4 8 10 18

Do the above satisfy case 1? Are they evenly spaced?

KarishmaB · Answer

Ok, look at this: 3, 5, 7, 9, 11

Mean = 7
Median = 7

I change the numbers a bit: 3, 4, 7, 10, 11 (Numbers are not evenly spaced now.)

Still, 
Mean = 7
Median = 7

Since mean depends on the overall sum of the numbers and median is just the middle number, there are very few constraints and how the numbers should be spaced for mean = median.

Non evenly spaced numbers can also have mean = median.

All evenly spaced numbers must have mean = median because here, mean is the middle number and median, by definition, is already the middle number.

alex1233 · Answer

Thank you guys it is clear now. Thanks a lot!!!

If the mean equals the median

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