The standard deviation is a measure of how much the numbers
differ from the mean on the average.
The smaller the standard deviation the closer the numbers are together.
The larger the standard deviation the more scattered out they are.
The mean (or ordinary average) of all three of the following data
sets is 50:
A. {50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50}
B. {45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55)
C. {0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
Data set A has a standard deviation of 0 because the numbers do not
differ at all from the mean 50. They are all the same, so the
standard deviation is zero because they don't deviate at all from 50.
Data set B has a standard deviation of about 3 because the numbers
average differing from the mean 50 by about 3. They are close together,
so the standard deviation is low.
Data set C has a standard deviation of about 30 because the numbers
average differing from the mean 50 by about 30. They are scattered out,
so the standard deviation is high.
Edwin
