Math whizes-what percentile is the mean?

[drmistga]

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So my stat days are long gone and I know there is no way to exactly know but given that they give you the SD and mean I know there is a way I just forgot-So for example what is the percentile of a 220 if the mean was 220-or whatever your test forms mean score and SD was-I am sure it is the same. Just curious since to me the mean ususally means nothing without a corresponding percentile as far as comparing scores. Ok thanks!

 

[NotThatOne]

So my stat days are long gone and I know there is no way to exactly know but given that they give you the SD and mean I know there is a way I just forgot-So for example what is the percentile of a 220 if the mean was 220-or whatever your test forms mean score and SD was-I am sure it is the same. Just curious since to me the mean ususally means nothing without a corresponding percentile as far as comparing scores. Ok thanks!

I'm not a math whiz. Don't even remember what I learned from stat. But here's my take:

If the scores are spread out fairly evenly, then the mean would correspond to approximately 50 percentile. However, the percentile can be higher or lower than 50% if the scores are not spread out evenly. This is especially true if the dataset is small.

Consider this set of scores: 10, 10, 10, 20, 20, 20, 25, 30, 35, 100, 100. The mean would be: 380/10 = 38. I would think a person with a score of 38 (mean score) would be somewhere in the 80 percentile in this set of scores. A median score would correspond more consistently with a 50 percentile.

 

[lord_jeebus]

I don't think there's an official median score out there so there's no way to say.

I would guess that the distribution has slight left skew (40 points under the mean seems more common than 40 points above it), with the mean's percentile being around 51.

This is pure speculation. For your calculation needs I'd just say it's 50.