Average Deviation Formula

Average Deviation Formula

The Average Deviation Formula assists you in computing the average from the mean by first calculating the difference between each value and the mean, followed by dividing the total by the sum of all the previously calculated values.

The Average Deviation Formula from the data set’s center is the average deviation of the data. When arranging the data set in order of decreasing to increasing values, the median value, also known as the exact center value, is used to calculate the distance from the mean. The mean represents the average value of all the numbers presented in the data set.

Other names for the average deviation value include meaning absolute deviation and average absolute deviation. Students can manually calculate the average deviation value for a small data group. Still, you will need to use a graphical program to determine the average deviation value for a large data set. With the aid of this software, you can quickly determine the average deviation value for a certain database sample. You only need to add the input of vast amounts of data to this software to determine the average deviation, and you will quickly receive the average deviation value after doing so.

What Is Average Deviation Formula?

In order to describe the dispersion among the measures in a particular population, statisticians utilize a variety of indices of variability, some of which include the 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. Additionally, it is known as an average absolute deviation.

How to Calculate Average Deviation?

Determine the mean, median, or mode value for the data set. The next step is to calculate the absolute difference between each value in the data set and the meanwhile disregarding signs. Following that, we add up all the deviations. The average or mean values discovered in Step 3 are what we locate last. The measure of deviation was found in the mean.

Solved Examples

A football player has played 5 games so far this season. The scoring numbers from each game are 14, 10, 9, 7, and 5. Determine the mean and calculate the average deviation.

Solution: The average of the score is = (14 + 10 + 9 + 7 + 5)/5 = 45/5 = 9

the average score = 9

To calculate the average deviation we need to calculate the deviation from the average for each game.

|14 – 9| = 5

|10 – 9| = 1

|9 – 9| = 0

|7 – 9| = 2

|5 – 9| = 4

Sum of variations = 5 + 1 + 0 + 2 + 4 = 12

Average deviation = 12/5 = 2.4

Answer: Hence the average deviation of the given data is 2.4

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FAQs (Frequently Asked Questions)

1. How Should the Data Mean Be Calculated in the Average Deviation Formula?

The average of the provided data set is determined by dividing the sum of observations by the total number of observations in the Average Deviation Formula.

2. How Can I Determine the Average Deviation Formula's xi - x?

The term (xi – x) in the Average Deviation Formula must be calculated since it yields the ultimate result, which is the average deviation of the given data. In order to calculate (xi – x), we must first determine the average of the provided data. The value of (xi – x) can be calculated separately by deducting the mean value from each observation.