How To Calculate Average Deviation (With Example and Steps)

Average deviation, combined with mean average, serves to help summarize a set of data. While mean average roughly gives the typical, or middle value, average deviation from the mean gives the typical spread, or variation in the data. College students will likely encounter this type of calculation in data analysis sections of laboratory reports or introductory statistics courses. Calculating the average deviation from the mean is easily done by hand with small data sets.

Calculating the mean average helps you determine the deviation from the mean by calculating the difference between the mean and each value. Next, divide the sum of all previously calculated values by the number of deviations added together and the result is the average deviation from the mean.

Calculating the mean average deviation.

How to calculate average deviation

Consider these steps when calculating the average deviation of a data set:

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.

What is average deviation?

The average deviation of a data set is an average of all deviations from a set central point. It is a statistical tool for measuring the distance from a mean or median, with the mean being the average value of all numbers in the data set and the median being the exact middle number when we order the data set from lowest to the highest number. The average deviation of a data set is also called mean absolute deviation (MAD) or average absolute deviation.

Although when working with relatively small sets of data you can calculate average deviation manually, larger data sets typically require special software that performs the calculations for you after you input the initial data.

Absolute deviation vs. average deviation

Calculating the absolute deviation is a crucial step for determining what the average deviation is. The absolute deviation is the difference between a data sets mean and each value in the respective data set. The name of absolute deviation comes from the fact that the resulting numbers are all written down as absolute numbers. The measure expresses the distance between the mean and each value, therefore it being a negative or positive number is irrelevant.

After calculating the absolute deviation for each value in the data set, you can calculate the average deviation by adding them all together and dividing them by the total number of values in the data set.

Example

Consider this example when calculating the average deviation from the mean.

A basketball player played 5 games so far this season. The scoring numbers from each game are 23, 30, 31, 15 and 46.

The first step is calculating the mean. You do this by adding the points and dividing the result by the five games.

*23+30+31+15+46=145*

*145/5=29*

Now that you determined that the player has scored an average of 29 points per game, you need to calculate the deviation from the mean for each game.

*23-29=6*

*30-29=1*

*31-29=2*

*15-29=14*

46-29=17

Next, you need to calculate the sum of all variations.

*6+1+2+14+17=40*

The average deviation is the sum of all deviations divided by the total number of entries.

*Average deviation=40/5=8*

The average deviation from the mean regarding the points scored in the first five games of the season is 8.

Mean average vs. average deviation from the mean

Calculating the mean average is also a crucial step in determining what the average deviation from the mean is. The mean average is simply the sum of all values included in the data set, divided by the total number of values. Calculating the mean average helps you determine the deviation from the mean by calculating the difference between the mean and each value. Next, divide the sum of all previously calculated values by the number of deviations added together and the result is the average deviation from the mean.

Standard deviation vs. average deviation

Standard deviation is also a measure of variability within a data set, as it shows the size of deviation between all values in the data set. The main difference between the two is that the resulting values from subtracting the mean from the value of each data point are only written as absolutes when calculating the average deviation. To calculate standard deviation, the resulting values are not written in absolutes, but squared. Then, you need to calculate the mean of all the squared values. The square root of that mean is the standard mean.

Standard deviation is more commonly used to measure variability, being a very popular tool to calculate the volatility of financial instruments and potential investment returns. Higher volatility typically means that there is an increased risk of an investment generating a loss, meaning that an investor that takes on the risk of high-volatility security typically expects a high return from it. The average deviation is also used as a financial tool, but typically less often than the standard deviation.

FAQ

What is the example of average deviation?

For example, let’s say the mean of your data set is 10, and you have 5 values: 1, 5, 10, 15 and 19. The absolute deviations are: 10 – 1 = 9. 10 – 5 = 5.

Is mean deviation and average deviation are same?

Mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean. Mean absolute deviation is a way to describe variation in a data set.

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