# Is there a way to calculate or estimate the trimmed mean given only summary statistics?

Lets say we have a set of arbitrary numbers, whose values range from $1$ to $100$

$$x = \{x_1,x_2,x_3,x_4,x_5,...,x_n\}$$

Given only the common summary statistics of $x$ (mean, standard deviation, variance), but not to $x$ itself.

Would it be possible to calculate or even estimate the trimmed mean (the mean excluding the lower and upper 10% of outliers) to a reasonable extent?

No, imagine 2 distributions, one a symmetric bell curve, and the other a spike centered at 50 with asymmetric outliers around 0 and 100. Their averages could both be 50, their standard deviations and variance could be the same, and their max and min would be the same, and their medians would be the same.

However, removing the outliers from the spiky distribution will change the mean, but the same is not true for the bell curve