Mean Absolute Deviation: Overview, Questions, Preparation

This chapter has multiple topics listed below:

Statistics Standard Deviation Correlation Bar Graph Chi Square Test Measures of Central Tendency Variance Extrapolation Null Hypothesis Pareto Chart Harmonic Mean How to find Median Statistics Definition Data Collection Methods Frequency Polygons Central Tendency Confidence Interval Data Handling Statistical Inference Quota Sampling Interquartile Range Quartiles Variance and Standard deviation Cluster Analysis Correlation and Regression Graphical Representation Least Square Method Level of Significance Paired T Test Z Score Table Assumed Mean Method Box and Whisker Plot Gamma Distribution Sample Size T Distribution Tests of Significance Types of Statistics Continuous Variable Sample Statistic Exponential Smoothing T Test Table Bivariate Analysis Relative Frequency Difference between Average and ...Difference between Mean and Med...Difference between Parametric a...Grouping data Statistics pdf Mean Absolute Deviation Population and Sample

Rachit Kumar SaxenaManager-Editorial

Updated on Aug 5, 2021 11:29 IST

Table of Contents

What is Mean Absolute Deviation (MAD)?
Weightage of Mean Absolute Deviation (MAD) in Class 11
Illustrative Example on Mean Absolute Deviation
FAQs on Mean Absolute Deviation

What is Mean Absolute Deviation (MAD)?

The definition of MAD is the process of finding it, which makes it super simple to remember.
Mean = Average of the observation
Deviation = Departure/variation from preset standard
Collectively, it is the distance between the calculated mean and each data point.

Simple Steps to Find MAD

STEP 1- Find the mean of the data.

Mean = Sum of the elements of the data set
------------------------------------------------
number of elements in the data set

STEP 2- Calculate how far each element is from the mean. Here, the absolute value used as the distance needs to always be a positive number.

MAD = Total the difference
-------------------------
Number of elements in the data set

What Does MAD Tell You?

In simple words, it indicates how far your data is spread. A large MAD indicates that the data set is more spread out relative to the mean.

Weightage of Mean Absolute Deviation (MAD) in Class 11

MAD is an integral part of the maths syllabus of Class 11 and is relevant not just for Class 11 exams, but also for various engineering exams such as JEE. You may well have explored the idea of chance in earlier classes as a measurement of the uncertainty of different phenomena. Here, focused on the class 11 maths syllabus, a summary of MAD is given, which will help to quickly learn the relevant terms and also to achieve good marks in exams.

Illustrative Example on Mean Absolute Deviation

1: Students of a class scored the following marks in an exam. Find the M.A.D of the Score.

55, 65, 70, 70, 72, 85, 90, 90, 93, 100

Solution:

The Mean of the given data

Mean = Sum of the elements of the data set
------------------------------------------------
number of elements in the data set

= 55 + 65 + 70 + 70 + 72 + 85 + 90 + 90 + 93 + 100 = 790
------------------------------------------------------------------- --------
10 10

Mean = 79

Calculate the deviation for the mean-

Marks	Deviation
55	55 - 79 = - 24
65	65 - 79 = - 14
70	70 - 79 = - 9
70	70 - 79 = - 9
72	72 - 79 = - 7
85	85 - 79 = 6
90	90 - 79 = 11
90	90 - 79 = 11
93	93 - 79 = 14
100	100 - 79 = 21

Mean Deviation = Sum of all the deviations from mean
----------------------------------------------
Total Number of Observations

Note: All the results that we get in negative need to be converted to positive numbers. This is done to reach conclusive results. For better understanding, if we use all the numbers exactly the way they were found, then it will give the following result:

[- 24 - 14 - 9 - 9 - 7 + 6 + 11 + 11 + 14 + 21 = 0]

The result is not giving any measurable value. These values in some cases may turn out to be [-number]. So, irrespective of the output being a negative value, it will be converted into a positive number and the Mean deviation will be found.

Mean Deviation= 24 + 14 + 9 + 9 + 7 + 6 + 11 + 11 + 14 + 21 = 126 = 12.6
----------------------------------------------------------- ------
10 10
This gives us a clear picture of the deviation of the observation from the centre. Thus, we can say that each score in the data set averages a distance of 12.6 from the mean of 79.

Generally, to calculate M.A.D (Mean Absolute Deviation) mean and median are used but any other measure of Central Tendency can also be used to calculate M.A.D.

FAQs on Mean Absolute Deviation

Q: What is the formula of Mean Deviation?

A: The formula is

Q: What is the formula of Mean Absolute Deviation?

A: The formula is

Q: What are the easy steps to calculate Mean Absolute Deviation?

A: The steps are as follows:
Step 1: Calculate the mean from the given observations.
Step 2: Find the difference between each observation and the calculated mean.
Step 3: Apply the formal to find the difference calculated from Step 2.

Q: How are you going to get the absolute mean deviation?

A: Start by taking the mean of the data set to find the mean absolute variance of the data. Find the sum of the values of the data, and split the sum by the number of values of the data. Locate the absolute value of the discrepancy between the value of each data and the mean value: |data value, mean|.

Q: Will there ever be a negative value to the mean absolute deviation?

A: If the MAD is zero, the absolute deviations are all zero. The average deviation from the mean is determined by the MAD and the distance is never negative. If all the absolute deviations are zero, the only way the MAD can average is to zero.