How to Calculate Percent Deviation

Percent deviation helps qualify the calculation of an average. For example, the average grade in a class may be a C, but no one in the class may have received a C. Instead, half the class received A's and the other half F's, which would result in an average C grade. Here, the deviation would be two letter grades, which tells us that most of the students received an A or an F. Percent deviation is often used in statistics and chemistry problems. It shows how far a measurement, on average, will deviate from the average (mean). A typical percent deviation problem gives a set of measured numerical data, such as the weight of female models. The student is then asked to find the percent deviation of the weight of female models from the average weight of a female model.

Instructions

    • 1

      Determine the average (mean) value of measurements. Sum the data values and then divide that number by the number of data values. Consider three measurements: 3, 4 and 8. The average value of these measurements is 5, since the sum of 3 plus 4 plus 8 is 15 and 15 divided by 3 is 5.

    • 2

      Calculate the average deviation. Find the deviation of each of the measurements from the mean, sum them and then divide by the number of measurements. The deviation from the mean of a value is defined as the absolute value of the difference between the value and the mean of the values. For the example above, the deviation of 3 from the mean of 5 is 2, since the absolute value of 3 minus 5 is 2. The deviation of 4 from the mean of 5 is 1, since the absolute value of 4 minus 5 is 1, The deviation of 8 from the mean is 3, since the absolute value of 8 minus 5 is 3.

      Remember that the absolute value of a number is always a positive number.

      Now sum the deviations of each measurement and divide that number by the number of measurements. For this example, the deviations are 2, 1 and 3, which total 6. So the average deviation is 2, since 6 divided by 3 is 2.

    • 3

      Calculate the percent deviation. Divide the average deviation by the mean and multiply by 100. For this example, the mean is 5 (from Step 1); the average deviation is 2 (from Step 2). So the percent deviation is 40 percent, since 2 divided by 5 is 0.4 and 0.4 times 100 is 40.

      This calculation tells you that on average, a randomly selected data value for this example data set (3, 4, 8) will be 40 percent from the mean. Specifically, either 3, since 5 minus 2 is three, or 7, since 5 plus 2 is seven. Remember that the average deviation calculated was 2 and that the mean was 5.

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