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To compute the Variance and Standard Deviation from a Frequency Distribution

Example:  The data here represents the three-year rate of return of a random sample of 40 small-capitalization growth mutual funds.  Approximate the variance and standard deviation three-year rate of return.

Press STAT and select 1: Edit. Clear L1 an L2. Enter the midpoints from the above table into L1 and the frequencies into L2. Press STAT, highlight CALC, select 1:1-Var Stats, and press 2^nd  , 2^nd ENTER. The sample statistics will appear on the screen. The sample standard deviation of the frequency distribution described in columns L1 and L2 is 9.2369. In this example you do not have the actual data. What you have is the frequency distribution of the data summarized into categories. The standard deviation of this frequency distribution is an approximation of the standard deviation of the actual data.

To calculate the sample variance,, type in the value of the standard deviation at the bottom of the screen and press the key and ENTER. The approximate sample variance is 85.32.