Question

For a skewed distribution, what is the approximate percentage of data values that are within 2 standard deviations

Answer 1

Chebyshev's Theorem can be used for a skewed distribution.

This theorem says:
1. Within two standard deviations of the mean, you will find at least 75% of the data.
2. Within three standard deviations of the mean, you will find at least 89% of the data.

Here's how the formula shows this:
Formula is 1 - (1/k^2) ---> ^2 means squared.

If k = 2 (representing two standard deviations), we have this:
1 - (1/2^2) = 1 - (1/4) = 3/4 or .75 or 75%

If k = 3 (representing three standard deviations), we have this:
1 - (1/3^2) = 1 - (1/9) = 8/9 or approximately .89 or 89%

I hope this helps.