Mean vs Median in Positive/Negative Skews

[g8orlife]

It makes sense to me that in a statistical distribution where there's a positive skew with a higher number of scores (mode) in the low end, that the average (mean) of all the scores would be less than the median.... but all my sources are saying that the mean is greater than the median.

Does anyone understand this?

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[makshim]

Think of neg/pos distributions it this way. The mean never changes, it's in the middle of the graph. The mode is at the highest point of the graph. The median is between the mean and mode.

 

[Frazier]

What are your sources?

Msar uses accepted student data. Us news uses matriculant data. School websites on case-by-case basis...

 

[g8orlife]

Think of neg/pos distributions it this way. The mean never changes, it's in the middle of the graph. The mode is at the highest point of the graph. The median is between the mean and mode.

I guess I don't understand why the mean doesn't change. If most of the scores are shifted to the either the high or low end, how is it that the mean stays the same?

Ex: If I have the normal/Gaussian distribution (1,2,2,3,3,3,4,4,5) then give it a Positive(Right) skew it could look like (1,1,2,2,2,3,3,4,5). How is the mean(average) still the same as before? Isn't the mean=3 in the original, but 2.5 after the skew?
Or am I thinking about this incorrectly?

What are your sources?...

First Aid, BRS Behavioral Health, HY Biostatistics

 

[lstone13]

I guess I don't understand why the mean doesn't change. If most of the scores are shifted to the either the high or low end, how is it that the mean stays the same?

Ex: If I have the normal/Gaussian distribution (1,2,2,3,3,3,4,4,5) then give it a Positive(Right) skew it could look like (1,1,2,2,2,3,3,4,5). How is the mean(average) still the same as before? Isn't the mean=3 in the original, but 2.5 after the skew?
Or am I thinking about this incorrectly?



First Aid, BRS Behavioral Health, HY Biostatistics

It may be easier to think about it by starting off with 2 groups of numbers with the same mean. Group A has a normal distribution with mean = median = mode. But group B has a positive skew (which means there are positive outliers). So in order for group B to have the same mean as group A, to compensate for its positive outliers, group B must have more values in the lower range. Because of this, the median will be lower than the mean in group B. Also consider what happens when you remove those positive outliers... The mean will automatically lower to come closer to its median and mode.

I hope this helps!

 

[g8orlife]

It may be easier to think about it by starting off with 2 groups of numbers with the same mean. Group A has a normal distribution with mean = median = mode. But group B has a positive skew (which means there are positive outliers). So in order for group B to have the same mean as group A, to compensate for its positive outliers, group B must have more values in the lower range. Because of this, the median will be lower than the mean in group B. Also consider what happens when you remove those positive outliers... The mean will automatically lower to come closer to its median and mode.

I hope this helps!

Ahh, Yeah that definitely helps!
Thanks for the great example. Crystal clear.