Question

It is possible to obtain a ""quick-and-dirty"" estimate of the mean of a normal distribution from the 50th percentile value on a normal probability plot. Provide an argument why this is so. It is also possible to obtain an estimate of the standard deviation of a normal distribution by subtracting the 84th percentile value from the 50th percentile value. Provide an argument explaining why this is so.

Answer 1

Explanation:

It is possible to obtain a ""quick-and-dirty"" estimate of the mean of a normal distribution from the 50th percentile value on a normal probability plot, because normal distribution curve is symmetrical about its mean with 50% on either side of the mean. Also it is unimodal, with mean = median = mode. Because of symmetrical shape, and other special properties we can obtain estimate of mean as the 50th percentile of any normal distribution.

Also in normal distribution 34% lie between mean and 1 std deviation on right side/left side

This gives 84th percentile is got by taking the z value on right side of mean.

When we subtract 84th percentile value from the 50th percentile value we really get -1 times std deviation. Hence to get std deviation actual value, without negative sign, we subtract (50-34) = 16th percentile from mean.