All is know is that the average of a data set (that i do not know ) is 22,2. And that is 95th percentile is 32,8.
Is it possible to calculate its 80th percentile with only this informations ?
Thank you in advance.
2026-03-26 07:58:29.1774511909
95th percentile of average
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The z-score formula is: $$z = \frac{x-\mu}{\sigma}$$ where $x$ is a point on the distribution, $\mu$ is the mean, and $\sigma$ is the standard deviation.
Since the z-score is related to a z-score table that maps the z-score to the percentiles with a one-to-one correspondence (bijection), if we know all three variables we can calculate the percentile.
We can randomly choose a point that we know on the curve, and we know the mean which is given in the question. However, the standard deviation is missing, so that is the only piece of information we need to calculate the $80$th percentile.