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.

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**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**.