# Average Deviation Formula

Last Updated : 14 Mar, 2024

Average Deviation is an effective way to analyze the variability in the given data. It is the average of all deviations from a central point. Average Deviation measures the distance from mean or median. It is also called Average Absolute Deviation (or) Mean Absolute Deviation.

Mean– It is the average value of all the values in the data.

Median– It is the middle value in the data when the data is sorted from low to high.

### Steps to calculate Average Deviation

Step 1. Calculate the mean or median value for given data.

Mean can be calculated by adding all the numbers in the given data and this total sum is divided by the count of all digits.

Median value can be calculated by sorting the data from low to high or high to low and picking the middle value. If the total count of numbers in given data is odd then the middle value will be the median. If the total count is even then there will be two middle numbers for these 2 numbers calculate the average of those two and the resultant value is the median of that dataset.

Step 2. Calculate the deviation from mean/median.

The deviation value can be calculated by calculating the absolute difference between each value in the data and the result of Step-1 i.e., mean or median value.

Step 3. Find the sum of all deviations of the result from the above step.

Step 4. Find the average of all deviations using the resultant sum of deviations and count of all values/deviations in the dataset. The final resultant average is the Average Deviation of the given data.

Let’s look at the few examples to understand better.

### Sample Questions

Question 1: Find the Average Deviation for the data 1,2,3,4,9,8,7,6.

Solution:

Step 1: Find the mean for the given data.

Mean=(Sum of all values)/(count of all values)

Mean = (1+2+3+4+9+8+7+6)/8

= 40/8 => 5

Step 2: Find absolute deviations from data using mean.

 Data Mean Deviation 1 5 abs(1-5) = 4 2 5 abs(2-5) = 3 3 5 abs(3-5) = 2 4 5 abs(4-5) = 1 9 5 abs(9-5) = 4 8 5 abs(8-5) = 3 7 5 abs(7-5) = 2 6 5 abs(6-5) = 1

Step 3: Sum of all deviations=4+3+2+1+4+3+2+1=20

Step 4: Find Average Deviation = sum of all deviations/count of values in data

= 20/8 => 5/4 => 1.25

So Average Deviation within the given data is 1.25

Question 2: Find the Average Deviation for the data 1,2,3,4,9,8,7,6. (Use median to find central point)

Solution:

Step 1: Find median for the given data.

To find the median first we need to sort the given data either in ascending order or descending order.

Sorted data- 1,2,3,4,6,7,8,9

Here the size of the data set is even i.e., count=8.

So we got two middle values 4 & 6.

Find the average of these two numbers to find the median value.

Median = (4+6)/2 = 5

Step 2: Find absolute deviations from data using median.

 Data Median Deviation 1 5 abs(1-5) = 4 2 5 abs(2-5) = 3 3 5 abs(3-5) = 2 5 5 abs(4-5) = 1 9 5 abs(9-5) = 4 8 5 abs(8-5) = 3 7 5 abs(7-5) = 2 6 5 abs(6-5) = 1

Step 3: Sum of all deviations = 4+3+2+1+4+3+2+1=20

Step 4: Find Average Deviation = sum of all deviations/count of values in data

= 20/8=> 5/4 => 1.25

So Average Deviation within the given data is 1.25

Question 3: Find the Average Deviation for the data 10,25,30,14,39,18,17. (Use median to find central point)

Solution:

Step 1: Find median for the given data.

To find median first we need to sort the given data either in ascending order or descending order.

Sorted data- 10,14,17,18,25,30,39

Here the size of data set is odd i.e., count=7.

So we have only one middle value18 which is median.

Step 2: Find absolute deviations from data using median.

abs(10-18) = 8

abs(14-18) = 4

abs(17-18) = 1

abs(18-18) = 0

abs(25-18) = 7

abs(30-18) = 12

abs(39-18) = 21

Step 3: Sum of all deviations = 8+4+1+0+7+12+21=53

Step 4: Find Average Deviation=sum of all deviations/count of values in data

=53/7=> 7.57

So Average Deviation within the given data is 7.57

Question 4: Find the Average Deviation for the data 10,20,30,40,39,28,17,10,20,26.

Solution:

Step-1 Find mean for the given data.

Mean=(Sum of all values)/(count of all values)

Mean=(10+20+30+40+39+28+17+10+20+26)/10

=240/10=>24

Mean=24

Step-2 Find absolute deviations from data using mean.

abs(10-24) = 14

abs(20-24) = 4

abs(30-24) = 6

abs(40-24) = 16

abs(39-24) = 15

abs(28-24) = 4

abs(17-24) = 7

abs(10-24) = 14

abs(20-24) = 4

abs(26-24) = 2

Step 3: Sum of all deviations=14+4+6+16+15+4+7+14+4+2=86

Step 4: Find Average Deviation=sum of all deviations/count of values in data

=86/10=> 8.6

So Average Deviation within the given data is 8.6

Question 5: Find the Average Deviation for the data 10,20,30,40,50 (Use mean/median to find central point)

Solution:

Step 1: Find the center point for the given data.

As data is already in sorted order it is preferred to use the median to find the central point.

Here the size of the data set is odd i.e., count=5.

So we have only one middle value 30 which is the median.

Step 2: Find absolute deviations from data using the median.

abs(10-30)=20

abs(20-30)=10

abs(30-30)=0

abs(40-30)=10

abs(50-30)=20

Step 3: Sum of all deviations=20+10+0+10+20 =60

Step 4: Find Average Deviation=sum of all deviations/count of values in data

=60/5=>12

So Average Deviation within the given data is 12.

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