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April 17, 2014

April 17, 2014

Posted by **mzb** on Tuesday, January 22, 2013 at 6:25pm.

- statistics -
**MathGuru**, Wednesday, January 23, 2013 at 6:27pmSome hints:

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%

Looking at your problem, the difference between the mean and the data given is 1.5 standard deviations.

Therefore, we have this:

1 - (1/1.5^2) = 1 - (1/2.25) = 1 - 0.44 = 0.56 = 56%

I hope this helps.

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