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From my understanding, mean = median if, 1. the set consists of evenly spaced numbers 2. if all the members of the set are equal 3. set has just one number

Is there any thing else? In DS type of "is mean = median" questions, what do you have to know to be sure that mean = median?

From my understanding, mean = median if, 1. the set consists of evenly spaced numbers 2. if all the members of the set are equal 3. set has just one number

Is there any thing else? In DS type of "is mean = median" questions, what do you have to know to be sure that mean = median?

Hi,

If a series is an arithmetic progression then mean value will always be equal to median, but vice versa is not true.

Thus, any series can be formed other than the ones you have mentioned where mean = median.

I did not say that the list that I provided is the exhaustive list. I just wanted add more to it. So if the Q is "is mean=median" What constitute sufficiency other than arithmetic progression and/or evenly spaced sets? Anything about the relationship that can be expressed in terms of range, relationship between the smallest or largest number, or the relationship between median and other numbers etc.?

Perhaps the easiest way to understand when mean = median is this one reqiurement:

1) When the distribution above the mean is symmetrical to the distribution below the mean.

So think of the middle point. Whatever pattern of data you have above the middle point is mirrored on the other side (below) the middle point.

When this happens, the mean will effectively be the same as the median (the middle number by rank).

This is satisfied when data is evenly spaced out. It's also true in other mirror-like cases.

Sure the distribution does not necessarily have to be exactly mirrored on both sides. But as long as they roughly cancel each other out, then you'll have a situation where the mean = median.
_________________

Median=Mean when: 1) Numbers are in a sequence i.e. evenly spaced (and that includes consecutive numbers) 2) Only one item in the set 3) All members of the set are equal

I've always thought of it like this, if you take the average of a group of evenly spaced numbers and that result is the middle number, then voila, mean = median.

For instance,

10, 20, 30, 50, 70, 80, 90

Mean = 50 Median = 50

Last edited by geometric on 27 Mar 2013, 11:45, edited 1 time in total.

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