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How to Calculate a Variance for Chemistry

Variance is a statistical tool for analyzing a series of measurements. Basically, it is a measure of how spread out the values are with respect to each other. If every single measurement is exactly the same, for example, then the variance is zero. By definition, the variance is equal to the average of the squared difference of each measurement from the mean of all the measurements.

Things You'll Need

Calculator

Instructions

- 1
  Add together all of the values and then divide the result by the number of values. As an example, say you are comparing the heights of five different pea plants, which are 4, 5, 7.5, 8.5, and 5 centimeters high, respectively. The sum total of these heights is 30. Thirty divided by 5 is 6, which is the mean value of all the plant heights.
- 2
  Starting with the first measurement, subtract the measured value from the mean of all the values and square the result. Don't worry if the subtraction yields a negative number -- the square of a negative number is always a positive number. In the pea plant example, subtract 4 from 6, for a result of 2. Square this result -- in other words, multiply 2 times 2 for a result of 4. Perform this calculation for each individual value. Doing so for the pea plant example yields a result of 4, 1, 2.25, 6.25 and 1.
- 3
  Average all the squared differences from the previous step. In other words, add up the results from the previous step and divide by the total number of measurements. For the pea plant example, 4 + 1+ 2.25 + 6.25 + 1 equals 14.5. Divide 14.5 by the total number of measurements, 5, for a result of 2.9. This number is the variance.

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