The standard deviation provides an important measure of variation in a set of data. The standard
deviation, loosely speaking, is the "typical" distance from a data value to the average of all data
values. The more distant data values are from the mean of the data, the larger the standard
deviation.
You should have learned how to compute the standard deviation of a set of numbers in your
introductory statistics class. In case you have forgotten or never learned, the example below
shows how to compute the standard deviation of a small data set. Usually we use a computer to
find standard deviations, but you will be required to find the standard deviation of a set of
numbers on some quiz and exam questions throughout the semester. Thus it is important that
you be able to compute standard deviations using your calculator. Many of you have a calculator
that will automatically compute the standard deviation of a set of numbers. The trick is to learn
how to input the data and ask the calculator to compute the standard deviation. Consult your
calculator manual to learn how to do this, or just compute the standard deviation by following the
steps in the example below.
Data: 1,3,8,12
1. Find mean: mean=(1+3+8+12)/4=6
2. Find deviations from mean:
1-6=-5
3-6=-3
8-6=2
12-6=6
3. Square the deviations from mean:
(-5)^2=25
(-3)^2=9
2^2=4
6^2=36
4. Sum the squared deviations:
25+9+4+36=74
5. Divide the result by one less than the number of observations:
74/(4-1)=24.66666666
6. Take the square root of the result to get the standard deviation:
sqrt(24.66666666)=4.967=standard deviation