# Average Deviation Calculator

Average deviation calculator can easily calculate the average deviation of any given data set. It can also find the mean value and count the data set observations.

``````<iframe src="https://calculatorhub.org/?cff-form=122" style="width:100%;height:100%;"></iframe>
``````

## What is Average Deviation?

Average deviation is a statistical tool that computes the mean of various variations in a data set. By measuring how far a deviation is from the mean or median of the data set, we can determine average deviation.

You can easily calculate the average deviation value for a small set of data manually, but if you want to find the average deviation value for a large set of data, you will need to use some illustration calculator tools.

## Average Deviation Calculator Use

• In the first field, enter the values from the data set. Make sure to comma-separate each value.
• It will show the average deviation of the entered data set as well as calculate the mean value.

## Average Deviation Formula

Average deviation for any data set can be found using the formula mentioned below.

Where,

n = total number of data values.
x = individual values in given data set.
x̄ = mean value.

## Examples on Finding Average Deviation

The formula given above can be used to get the dataset’s average deviation. Below, we’ve tried to explain a few examples that will help you understand how the formula functions.

Example :

1. Using the average deviation formula, calculate the average deviation of the following data: 8, 16, 32, 64, 128.

Solution :

We have given dataset value (x) = 8, 16, 32, 64, 128.

Total number of values (n) = 5.

We can now find the mean value of the data set. To find the mean just divide the sum of all observations by the total number of observations.

Mean (x̄) = (8+16+32+64+128) / n
Mean (x̄) = (8+16+32+64+128) / 5
Mean (x̄) = 248 / 5
Mean (x̄) = 49.6

we have also created a arithmetic mean calculator which quickly calculates the mean value of large data values.

Using the average deviation formula,

Average deviation = (1/n)Σ |x – x̅|
Average deviation = ( |8-49.6| + |16-49.6| + |32-49.6| + |64-49.6| + |128-49.6| ) / 5
Average deviation = ( |-41.6| + |-33.6| + |-17.6| + |14.4| + |78.4| ) / 5
Average deviation = (41.6 + 33.6 + 17.6 + 14.4 + 78.4) / 5
Average deviation = 185.6 / 5
Average deviation = 37.12

Average Deviation of the dataset 8, 16, 32, 64, 128 is 37.12.

Example :

2. This season, a hockey player has played in seven games. Each game’s scoring figures are 4, 9, 12, 1, 3, 1, and 5. Calculate the mean and the average deviation.

Solution :

We have given dataset value in the form of each game’s scoring figures (x) = 4, 9, 12, 1, 3, 1, 5.

Total number of values (n) = 7.

We can now find the mean value of the data set. To find the mean just divide the sum of all observations by the total number of observations.

Mean (x̄) = (4+9+12+1+3+1+5) / n
Mean (x̄) = (4+9+12+1+3+1+5) / 7
Mean (x̄) = 35 / 7
Mean (x̄) = 5

Using the average deviation formula,

Average deviation = (1/n)Σ |x – x̅|
Average deviation = ( |4-5| + |9-5| + |12-5| + |1-5| + |3-5| + |1-5| + |5-5| ) / n
Average deviation = ( |-1| + |4| + |7| + |-4| + |-2| + |-4| + |0| ) / 7
Average deviation = (1 + 4 + 7 + 4 + 2 + 4 + 0) / 7
Average deviation = 22 / 7
Average deviation = 3.143

Average Deviation of the dataset 4, 9, 12, 1, 3, 1, 5 is 3.143.
Mean Value of the dataset 4, 9, 12, 1, 3, 1, 5 is 5.