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Counting by Units of Standard Deviation

Though we don't need to know how to calculate standard deviation, we do need to know how to use it. The standard deviation of a certain list is always expressed along with the average of the same list.

For example, one might say that the average gambler's winning in Las Vegas is $200, with a standard deviation of $30. It is then possible to count in units of standard deviation. One standard deviation would be $30, two standard deviations would be 2 x 30 = $60, and three standard deviations would be 3 x 30 = $90.

Example

Farmers in the United States grew an average (arithmetic mean) of 80 tons of corn each, with a standard deviation of 10 tons. What value is two standard deviations away from the mean?

A)  90

B) 82

C) 78

D) 75

E) 60

Answer: 60

Since the standard deviation is 10, two standard deviations is 2x10=20. Standard deviations can be counted above and below the average, which, in this case, is 80. So two standard deviations away from 80 would be 20 tons less or more. 80 ­ 20 = 60.

Standard Deviation in Practical Use

Standard Deviation is called “standard” because the results are standardized. This means that one standard deviation in a given list has the same statistical meaning as one standard deviation in another list. The percentage of the population at any standard deviation is always the same:

Between + 1 and ­ 1: 68%

Between + 2 and ­ 2: 95%

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