What's the formula for average deviation​

1. Calculate the mean/median

The first step is calculating the mean. You can do that by adding all the values in the data set and dividing the resulted sum by the total number of values.

Alternatively, you can calculate the median if you wish to use it instead of the mean. Arrange all numbers in numerical order and count how many there are in total. Then, if the total number is an odd one, divide it by two and round up to find the position of the median. If the total number is even, divide it by two and make an average between the number in that position and the one in the next higher position.

2. Calculate the deviation from the mean

After calculating the mean, you can calculate the deviation from the mean for each value in the data set. Calculate the difference between the previously calculated mean and each value in the data set and write down the absolute value of the resulting numbers. The absolute value of a number is its modulus or non-negative value. Since the direction of each variation is irrelevant when calculating the average deviation, all resulting numbers are positive.

3. Calculate the sum of all deviations

After calculating the deviation from the mean for each value in the data set, you need to add them together. Since this is an absolute value operation, each value should be a positive number.

4. Calculate average deviation

Finally, calculate the average deviation of your data set by dividing the previously calculated sum of all deviations by the total number of deviations that you added together. The resulting number is the average deviation from the mean.

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