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Median = Average when??

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by Ian Stewart » Tue Aug 24, 2010 3:47 pm
HPengineer wrote:When does the median of a set of numbers = the average of the set?

Do the sets have to be consecutive or evenly spaced for this rule to apply?
When a set is evenly spaced, the median and average are always equal. The 'converse' is *not* true; if the median and average are equal, the set may or may not be evenly spaced. For example, this set:

{0,1,50,99,100}

has a median and mean of 50, but is clearly not evenly spaced.
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by HPengineer » Tue Aug 24, 2010 3:50 pm
Does the evenly spaced set have to have an odd or even number of integers in the set?

or is the key simply that they are evenly spaced integers then Median = average?
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by Ian Stewart » Tue Aug 24, 2010 6:01 pm
HPengineer wrote:Does the evenly spaced set have to have an odd or even number of integers in the set?

or is the key simply that they are evenly spaced integers then Median = average?
No restrictions: if a set is evenly spaced, the average equals the median.
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