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This would be expected in a very Normal distribution, but there are some skewed statistical distributions where you would not expect that to be the case. For e
by cuckcuckspruce 11y ago
This would be expected in a very Normal distribution, but there are some skewed statistical distributions where you would not expect that to be the case. For example, if you're doing an analysis of the following data:
1, 2, 3, 4, ..., 98, 1000000, 1000000 then the mean would be 2,004,851 / 100 = 20048.51. In that case, 98% of your sample points fall below the mean.
- mikeash 11y agoRight, but apparently this distribution is not particularly skewed, since close to half of the values are below the median. And since distributions where the mean and median line up are common and expected, it's really weird to say that the mean is misleading because of that. I suspect/hope the reviewer meant to say that the use of the mean is misleading because the lower values somehow don't support whatever conclusion was reached.
- cuckcuckspruce 11y agoThat's most likely, and I agree that it's likely in the case mentioned that the data is not skewed. However, the main reason I posted is because the post I was responding to appeared to make the assumption that nearly half of the data points will always be below the mean, and I was pointing out that there are some distributions where you should not expect that to be the case because they are skewed.
- laumars 11y agoI made no such assumption. Why would you even assume that I expect this to always be the case? As already pointed out, it's pretty easy to make an assumption about this specific example since we're told that close to half of the values are below the median.