Standard Deviations
The Standard Deviation is a measure of how spread out numbers are (read that
page for details on how to calculate it).
When you calculate the standard deviation of your data, you will find that
(generally):
68% of values are within
1 standard deviation of the mean
95% of values are within
2 standard deviations of the
mean
99.7% of values are within
3 standard deviations of the
mean
Example: If the average height of men in the United States is 69 inches
and the standard deviation is 3 inches then you can say that 68% of men in
the United States are between 66 inches and 72 inches. Add and subtract
the standard deviation of 3 inches to the mean of 69 inches to obtain this
statistic.
Question 1: The mean height of women in the United States is 54 inches
with a standard deviation of 2.5 inches. Find the height range in which 95%
of women fall.
Question 2: The mean SAT Math score is 510 with a standard deviation of
115. Find the range in which 99.7% of scores fit. Does your answer have a
natural conflict with reality?
Question 3: 95% of automobiles sold in the US will achieve 10 mpg to 38
mpg. What is the mean and standard deviation of the gas mileage of a new
car?