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How to Calculate the Variance Estimate for Data

Variance is a measure of imprecision. Variance is the standard deviation squared. A report of the variance of a data set implies that the data are normally distributed. If the data are not normally distributed, a variance misrepresents the dispersion. We will use the following ages of second graders for the examples: 5, 7, 6, 8, 7.

Things You'll Need

  • Calculator or computer with spreadsheet
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Instructions

  1. Calculating a Variance Manually

    • 1

      Calculate the average of your data.

      For the example, the average = (5 + 7 + 6 + 8 + 7)/5 = 6.6

    • 2

      Calculate the deviations of the data and square them.

      The deviations are the differences of the individual data points from the mean. For example, where "^2" means squared: 5 - 6.6 = - 1.6; - 1.6 ^ 2 = - 1.6 x - 1.6 = 2.56

      For our data set, the squared deviations are:

      ( 5 - 6.6) ^ 2 = 2.56

      ( 7 - 6.6) ^ 2 = 0.16

      ( 6 - 6.6) ^ 2 = 0.36

      ( 8 - 6.6) ^ 2 = 1.96

      ( 7 - 6.6 ) ^ 2 = 0.16

    • 3

      Add the square of the deviations.

      2.56 + 0.16 + 0.36 + 1.96 + 0.16 = 5.20

    • 4

      Divide the sum of the deviations squared by the number of data points minus 1 to get the variance.

      5.20 / (5 - 1) = 1.3

      The units of the variance are the same as the original data set, so the variance in this example is 1.3 years.

    Calculating Variance in Microsoft Excel

    • 5

      Enter the numbers 5, 7, 6, 8 and 7 in cells A1 through A 5, respectively.

    • 6

      Click on Cell A7 and type "=var(a1:a5)" without the quotation marks.

    • 7

      The result "1.3" will appear.

    Other Ways to Calucate Variance in Microsoft Excel

    • 8

      Click on the symbol "fx" by the function tool bar.

    • 9

      Type in "VAR" or clear out the instructions in the window by hitting the "Delete" key on the keyboard when the instructions are highlighted in black. If you have clicked on the window already, highlight the instructions and hit "Delete" or use the backspace key after placing the cursor at the end of the instructions. Then type in "VAR."

    • 10

      Click on the "GO" button.

    • 11

      Click on the word "VAR."

    • 12

      Click "OK." A pop-up window with two active lines labeled "Number 1" and "Number 2" will appear.

    • 13

      Type in the number "5." If the instructions are still present, highlight the instructions and press "Delete," or place the cursor at the end of the instructions and use the backspace key.

    • 14

      Click on the entry line to the left of the line labeled "Number 2." Notice that a new line labeled "Number 3" appears.

    • 15

      Click on the entry line to the right of the line labeled "Number 2."

    • 16

      Type "7" in the line.

    • 17

      Repeat Steps 8 and 9 with the numbers 6, 7 and 8, entering each in a new "Number" line.

    • 18

      When you have finished typing in your data, click "OK." The number "1.3," which is the variance of this data set, will appear.

    • 19

      The entry of individual data as described in Steps 1 through 12 could also be accomplished by selecting a free cell and typing "=var(5,7,6,8,7)" and then pressing the "Enter" key.

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