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Average Deviation Formula

Last updated date: 20th Jun 2024
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Average Deviation Formula- Overview

The average deviation formula helps you to calculate the average from the mean by calculating the difference between the mean and each value, after that dividing the sum of all the values that were previously calculated by the number of deviations that are added all together.

The average deviation of the data is the average of all the deviations from the central point of the set. For measuring the distance from mean or median with taking mean as the average value of all the numbers presented in the data set and median being the exact center value or you can refer to it as the middle value of the data set when it is arranged in the order of decreasing to increasing values. The average deviation value can also be referred to as the mean absolute deviation or average absolute deviation.

If you are calculating the average deviation value for a small set of data you can easily do it manually but if you are looking for finding the average deviation value of some large set of data, you need to use some illustration softwares. This software will help you to find the average deviation value for a particular sample of the database easily. In this software, you just need to add the input of large data for which you need to find the average deviation and you will easily receive the average deviation value just by adding the input of the data in the softwares.

Now let us look at the other information related to the average mean deviations provided to you by Vedantu in this article.

Average Deviation 

The average deviation is actually the deviation of all the data in the set from its central point. It is the process by which you can easily measure the difference between mean and median. Here the mean is the average of all the numbers presented in the set while the median is the exact center or the middle number of the set that we get after arranging the values in ascending order, that is, from lower to higher.

How to Calculate Average Deviation from Mean

The arithmetic average of the deviations (all taking positive) from the mean, median or mode is known as average deviation or mean deviation.

Average deviation from ungrouped data or individual series is given by 

Average deviation = \[\frac{1}{N}\sum_{i=1}^{n}\mid x_{i}-m \mid\] 

where, \[\sum_{i=1}^{n}\mid x_{i}-m \mid\] is the sum of modulus of the deviation of the variate from the mean (mean, median or mode) and N is the number of terms.

There are several methods by which you can actually calculate the average deviation of the values present in the set they can be as follows

  1. By calculating the mean and median: you can calculate the mean of the values by adding all the values in the data and then dividing it by the total number of values.

You can calculate the median in the same way that is when you will arrange the value in the order lower to higher middle value will be median.

  1. Calculating the deviation from mean: After calculating the mean you can calculate the deviation from the mean  by calculating the difference between previously calculated mean and each value mentioned in the data set.

  1. Calculating the sum of all the deviations: After you calculate the deviation of each value you are required to add all the deviations that you get.

  1. Calculating the average deviation: The final step is to calculate the average deviation that is by dividing the sum of all deviations with the total number of deviations that are added.

Example: The score of batsmen in ten innings are 38, 70, 48, 34, 42, 55, 63, 46, 54, 44. Find the mean deviation about the median. 

Sol: Arranging the data in ascending order.

We have 34, 38, 42, 44, 46, 48, 54, 55, 63, 70.Here n = 10.

So, the median is the A.M. of 5th and 6th observation.

⸫ Median M = \[\frac{46+48}{2}\]=47

Average deviation   =

\[\frac{\mid 38-47\mid +\mid 70-47 \mid +\mid 48-47\mid+\mid 34-47\mid  }{10}\]

\[\frac{\mid 42-47\mid +\mid 55-47 \mid + \mid 63-47 \mid + \mid 46-47 \mid +\mid 34-47 \mid  }{10}\]+\[\frac{\mid 54-47\mid+ \mid 44-47 \mid }{10}\] +\[\frac{\mid 54-47\mid+ \mid 44-47 \mid }{10}\]

 = \[\frac{86}{10}\] = 8.6  

Practice Question

Calculate the average deviation about mean for the given data 4, 6, 8, 10, 12, 14.

  1. 37.5

  2. 38

  3. 40

  4. 42.

FAQs on Average Deviation Formula

1. What is the use of average deviation?

Average deviation is used as the measure of dispersion and within the group inter rated arguments.This average deviation can be referred to as average mean deviation or you can simply say it as mean deviation. This value is calculated mainly by finding the mean and median of the sets first and then from mean and median you can easily calculate the absolute average deviation. This is often used by the statistics to calculate the dispersion among the measures in the given population.

2. What is the average deviation in terms of variability?

This is used to tell you about the average , that means it is used to tell how far a particular score lies from its mean value. The larger will be the standard deviation, it indicates that the larger is the variability of the data, meaning the data set is more variable. You can  refer to variability as the spread or scattering of the data. The most commonly variability is measured with:

  • Range

  • Interquartile Range 

  • Standard deviation

  • Variation

3. What is the Difference between the average deviation and the standard deviation?

The standard deviation is also to calculate the spread of data over the mean which is somewhat similar to that of average absolute deviation. Roughly thinking about the average deviation, we can say it to be the average distance of the data from the mean value. In other words if we talk about the standard deviation it is approximately equal to the average deviation or average absolute deviation. You can calculate it by finding the mean first and then by arranging the data in the particular order you can find the median value , that is ,the muddle value and finally you can calculate the deviation.

4. Do we have any particular units for average deviations?

Standard deviation or we say about the absolute average deviation is calculated by first calculating the mean of all the data that you are provided with, after that you can arrange the data in a particular order and then you can find its middle value. The middle value is known as the median. From the mean and median you can calculate the average deviation of a data set provided to you. Now, if we talk about the units of the standard deviation, then the average deviation has the same value of units, tags if the units are the same as that of any value that is there in the set.

5. What are the benefits of having g noyes of average deviation from vedantu?

Vedantu provides you with all the notes that are specially designed by the experts for the help of the students. They are going to help you to score well and along with it these notes will help you to increase your knowledge. The experts have created these notes by taking into consideration the capabilities and the needs of the students. These notes not only provide you with the basic information but also clears most of your doubts so that for a topic you may not be having any remaining doubt and the concept is clear in your head and you can perform well if any question from the topic comes in your examination.