The Consequences Of A Deviation
You perform a series of coin-flipping experiments, each time flipping a fair coin 10 times and recording the number of heads. You perform 8 such experiments and record the results. 1 time there were 3 heads, 6 times there were 5 heads, and 1 time there were 7 heads.
You proceed to calculate the mean and the standard deviation of your results. What percentage of your results were strictly less than 2 standard deviations away from the mean?
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1 solution
The mean is ( 3 + ( 6 ∗ 5 ) + 7 ) / 8 = 4 0 / 8 = 5 .
The standard deviation is ( ( 3 − 5 ) 2 + 6 ( 5 − 5 ) 2 + ( 7 − 5 ) 2 ) / 8 = 1
So strictly less than 2 standard deviations covers the interval (3, 7), which contains 6 of the 8 results, or 75% of the results.