Calculating the mean average deviation.
How to calculate average deviation
When determining a data set’s average deviation, take into account the following steps:
1. Calculate the mean/median
The first step is calculating the mean. To do that, add up every value in the data set, then divide that total by the number of values.
If you want to use the median instead of the mean, you can calculate the median instead. Place all figures in numerical order, then total them all up. If the total number is odd, divide it by two and round up to determine where the median is located. Make an average between the number in that position and the number in the position above it if the total is even.
2. Calculate the deviation from the mean
You can determine the deviation from the mean for each value in the data set after determining the mean. Determine the difference between each value in the data set and the previously calculated mean, then record the absolute value of the resulting numbers. A number’s modulus, or non-negative value, is its absolute value. The average deviation is calculated regardless of the direction of each variation, so all resulting numbers are positive.
3. Calculate the sum of all deviations
You must add the deviation from the mean for each value in the data set after calculating it for each individual value. Each value should be a positive number because this is an absolute value operation.
4. Calculate average deviation
Finally, determine the average deviation of your data set by dividing the total number of deviations that you added together by the sum of all deviations that you previously calculated. The resulting number is the average deviation from the mean.
What is average deviation?
A data set’s average deviation is the average of all departures from a predetermined central point. It is a statistical tool for calculating the deviation from a mean or median, where the mean is the average of all the data’s numbers and the median is the exact middle number when the data are arranged from lowest to highest. The mean absolute deviation (MAD) or average absolute deviation are other names for the average deviation of a data set.
Although you can calculate average deviation manually when working with relatively small data sets, larger data sets typically require specialized software that does the calculations after you input the initial data.
Absolute deviation vs. average deviation
Finding the average deviation requires first calculating the absolute deviation. The difference between a data set’s mean and each value in that data set is known as the absolute deviation. The fact that the resulting numbers are all expressed as absolute numbers gives absolute deviation its name. Whether the measure is positive or negative doesn’t matter because it represents the distance between each value and the mean.
You can determine the average deviation after determining the absolute deviation for each value in the data set by adding all of them together and dividing by the total number of values in the data set.
Example
When calculating the average deviation from the mean, take into account this illustration.
A basketball player played 5 games so far this season. Each game’s scoring results are 23, 30, 31, 15, and 46.
The first step is calculating the mean. To do this, add the points together and divide the total by the number of games.
*23+30+31+15+46=145*
*145/5=29*
Calculate the deviation from the mean for each game after determining that the player has scored an average of 29 points per 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 calculated by dividing the total number of entries by the sum of all deviations.
*Average deviation=40/5=8*
In terms of the points scored in the season’s first five games, the average deviation from the mean is 8 points.
Mean average vs. average deviation from the mean
Another critical step in figuring out the average deviation from the mean is to calculate the mean average. The sum of all values in the data set divided by the total number of values yields the mean average. By calculating the difference between the mean and each value, calculating the mean average aids in determining the deviation from the mean. The average deviation from the mean is then calculated by dividing the total of all previously calculated values by the total number of deviations.
Standard deviation vs. average deviation
Standard deviation, which depicts the size of deviation between all values in the data set, is another indicator of variability within a data set. The primary distinction between the two is that when calculating the average deviation, the values obtained by deducting the mean from the value of each data point are only expressed as absolutes. The resulting values are squared instead of written in absolute terms to determine standard deviation. The mean of all the squared values must then be determined. The square root of that mean is the standard mean.
The standard deviation is a measure of variability that is more frequently used, and it is a widely used tool to determine the volatility of financial instruments and potential investment returns. An investor who accepts the risk of a high-volatility security typically expects a high return from it because higher volatility typically entails an increased risk of an investment producing a loss. In addition to the standard deviation, the average deviation is also employed as a financial tool, though less frequently.
FAQ
What is average deviation?
Calculating the mean and then the precise distance between each score and that mean without taking into account whether the score is above or below the mean yields the average deviation of a set of scores. It is also called an average absolute deviation. Below mentioned is the formula to calculate the average deviation.
Is average deviation and mean deviation same?
Let’s say your data set has a mean of 10, and you have the following five values: 1, 5, 10, 15, and 19. The absolute deviations are: 10 – 1 = 9. 10 – 5 = 5.
