For any set of data population or sample with sample size gr

For any set of data (population or sample) with sample size greater than 1, regardless of the data distribution, the proportion of the data that must be within k standard deviations on either side of the mean follows the following (Chebyshev’s Inequality): P{ |x - | 2 At least ______% of the data fall in the interval from - 3 to + 3 Do not include % sign; that is, for 0.1210 or 12.1%, put 12.1. Give answer accurate to at least three decimals or the first decimal in terms of percentages.

Solution

Note that at least 1 - 1/k^2 lie within k standard deviations from the mean.

Thus, as k = 3 here,

1 - 1/k^2

= 1 - 1/3^2

= 0.88888889

or

= 88.88889% [ANSWER]