VarianceAnother measure of dispersion is the variance. It is one of the most helpful measures because it assigns more weight to those pieces of data that are farther in value from the mean.
The formula for variance, abbreviated Var, is:
Var = frac{sum (x_i-overline{x})^2}{n} ,
where x_i are the data values, overline{x} is the mean or average, and n is the number of pieces of data.
Using a chart to organize the information and calculations is extremely helpful when there is a lot of data.
 
Let's look at an example to see how to find the variance for a set of numbers:
James was planning a ski trip and was interested in finding out some "cool" information about the venues he might select.
He discovered the following information:
Record Single Day SnowfallCrescent, Oregon
1950
40.0 inches
Lyons Falls, New York
1988
47.5 inches
Park City, Utah
1968
33.0 inches
Randolph, New Hampshire
1969
49.3 inches
South Fork, Colorado
1997
55.0 inches
South Lake Tahoe, California
1958
45.0 inches
Vale, South Dakota
1894
48.0 inches
West Yellowstone, Montana
1962
24.0 inches
Whittier, Alaska
1959
44.0 inches
 
Find the variance for this data set.
1. Find the mean: overline{x} =frac{40+47.5+33+49.3+55+45+48+24+44}{9} = frac{385.8}{9} =42.8overline{666} For convenience, let's round 42.8overline{666} to 42.9
2. Let's look at the table we will need for the problem: List the data in the left column, the mean in the second column, their difference in the third column and the square of that difference in the last column.
 
3. To find the variance, find the sum of the values in the last column and then divide by the number of data values.
text{Var}=frac{sum (x_i-overline{x})^2}{n} = frac{8.41+21.16+98.01+40.96+146.41+4.41+26.01+357.21+1.21}{9}
=frac{703.79}{9} =78.19overline{888}
Rounded to the nearest tenth, we get: text{Var} = 78.2