Mean Deviation | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year PDF Download

 Page 1


Mean Deviation 
 
The mean deviation (also known as Mean Absolute Deviation, or MAD) of 
the data set is the value that tells us how far each data is from the center 
point of the data set. The center point of the data set can be the Mean, 
Median, or Mode. Thus, the mean of the deviation is the average of the 
absolute deviations of all data points from the chosen central value. 
Key Concepts 
1. Central Tendency 
? The central point of a dataset can be represented by the 
Mean, Median, or Mode. 
? Mean Deviation measures how far the data points are 
spread out from this central value. 
2. Absolute Deviation: 
? The absolute deviation of a data point is the absolute 
difference between the data point and the central value 
( |xi-central value ||xi -central value |). 
? Using absolute values ensures that deviations are always 
positive, regardless of direction. 
3. Mean of Deviations: 
? The Mean Deviation is the average of all absolute 
deviations in the dataset. 
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Mean Deviation 
 
The mean deviation (also known as Mean Absolute Deviation, or MAD) of 
the data set is the value that tells us how far each data is from the center 
point of the data set. The center point of the data set can be the Mean, 
Median, or Mode. Thus, the mean of the deviation is the average of the 
absolute deviations of all data points from the chosen central value. 
Key Concepts 
1. Central Tendency 
? The central point of a dataset can be represented by the 
Mean, Median, or Mode. 
? Mean Deviation measures how far the data points are 
spread out from this central value. 
2. Absolute Deviation: 
? The absolute deviation of a data point is the absolute 
difference between the data point and the central value 
( |xi-central value ||xi -central value |). 
? Using absolute values ensures that deviations are always 
positive, regardless of direction. 
3. Mean of Deviations: 
? The Mean Deviation is the average of all absolute 
deviations in the dataset. 
Mean Deviation Example 
If we have to ?nd the mean deviation of the data set, {4, 5, 6, 7, 8}. 
? Calculate Value (Mean): 
Mean = (4 + 5 + 6 + 7 + 8)/5 = 6 
? Now we subtract the mean from each data set to obtain the 
deviation from the mean. 
Values 
Absolute Deviation from 
Mean 
|value – mean| 
4 2 
5 1 
6 0 
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Mean Deviation 
 
The mean deviation (also known as Mean Absolute Deviation, or MAD) of 
the data set is the value that tells us how far each data is from the center 
point of the data set. The center point of the data set can be the Mean, 
Median, or Mode. Thus, the mean of the deviation is the average of the 
absolute deviations of all data points from the chosen central value. 
Key Concepts 
1. Central Tendency 
? The central point of a dataset can be represented by the 
Mean, Median, or Mode. 
? Mean Deviation measures how far the data points are 
spread out from this central value. 
2. Absolute Deviation: 
? The absolute deviation of a data point is the absolute 
difference between the data point and the central value 
( |xi-central value ||xi -central value |). 
? Using absolute values ensures that deviations are always 
positive, regardless of direction. 
3. Mean of Deviations: 
? The Mean Deviation is the average of all absolute 
deviations in the dataset. 
Mean Deviation Example 
If we have to ?nd the mean deviation of the data set, {4, 5, 6, 7, 8}. 
? Calculate Value (Mean): 
Mean = (4 + 5 + 6 + 7 + 8)/5 = 6 
? Now we subtract the mean from each data set to obtain the 
deviation from the mean. 
Values 
Absolute Deviation from 
Mean 
|value – mean| 
4 2 
5 1 
6 0 
7 1 
8 2 
? Sum of Absolute Deviations: 
2 + 1 + 0 + 1 + 2 = 6 
? Mean Deviation: 
Mean Deviation = 6/5 = 1.2 
This gives the mean deviation of the given data set. 
Mean Deviation Formula 
There are various types of mean deviation formulas used depending upon the 
types of data given and the central point chosen for the given data set. We 
have different formulas for grouped data, and ungrouped data, also the mean 
deviation formula is different for deviation about mean and the deviation 
about median or mode. The image added below shows the mean deviation 
formula in various cases. 
Page 4


Mean Deviation 
 
The mean deviation (also known as Mean Absolute Deviation, or MAD) of 
the data set is the value that tells us how far each data is from the center 
point of the data set. The center point of the data set can be the Mean, 
Median, or Mode. Thus, the mean of the deviation is the average of the 
absolute deviations of all data points from the chosen central value. 
Key Concepts 
1. Central Tendency 
? The central point of a dataset can be represented by the 
Mean, Median, or Mode. 
? Mean Deviation measures how far the data points are 
spread out from this central value. 
2. Absolute Deviation: 
? The absolute deviation of a data point is the absolute 
difference between the data point and the central value 
( |xi-central value ||xi -central value |). 
? Using absolute values ensures that deviations are always 
positive, regardless of direction. 
3. Mean of Deviations: 
? The Mean Deviation is the average of all absolute 
deviations in the dataset. 
Mean Deviation Example 
If we have to ?nd the mean deviation of the data set, {4, 5, 6, 7, 8}. 
? Calculate Value (Mean): 
Mean = (4 + 5 + 6 + 7 + 8)/5 = 6 
? Now we subtract the mean from each data set to obtain the 
deviation from the mean. 
Values 
Absolute Deviation from 
Mean 
|value – mean| 
4 2 
5 1 
6 0 
7 1 
8 2 
? Sum of Absolute Deviations: 
2 + 1 + 0 + 1 + 2 = 6 
? Mean Deviation: 
Mean Deviation = 6/5 = 1.2 
This gives the mean deviation of the given data set. 
Mean Deviation Formula 
There are various types of mean deviation formulas used depending upon the 
types of data given and the central point chosen for the given data set. We 
have different formulas for grouped data, and ungrouped data, also the mean 
deviation formula is different for deviation about mean and the deviation 
about median or mode. The image added below shows the mean deviation 
formula in various cases. 
 
Where, 
? ? – Summation 
? xi – Observations 
? µ  – Mean 
? n – Number of observations 
Mean Deviation Formula for Ungrouped Data 
For ungrouped data or data that is not properly arranged that is the given 
data is in raw form, the mean deviation is calculated using the formula, 
Mean Deviation = ?i = 1n |xi – x ¯ | / n 
 
 
where, 
? xi represents the ith observation 
Page 5


Mean Deviation 
 
The mean deviation (also known as Mean Absolute Deviation, or MAD) of 
the data set is the value that tells us how far each data is from the center 
point of the data set. The center point of the data set can be the Mean, 
Median, or Mode. Thus, the mean of the deviation is the average of the 
absolute deviations of all data points from the chosen central value. 
Key Concepts 
1. Central Tendency 
? The central point of a dataset can be represented by the 
Mean, Median, or Mode. 
? Mean Deviation measures how far the data points are 
spread out from this central value. 
2. Absolute Deviation: 
? The absolute deviation of a data point is the absolute 
difference between the data point and the central value 
( |xi-central value ||xi -central value |). 
? Using absolute values ensures that deviations are always 
positive, regardless of direction. 
3. Mean of Deviations: 
? The Mean Deviation is the average of all absolute 
deviations in the dataset. 
Mean Deviation Example 
If we have to ?nd the mean deviation of the data set, {4, 5, 6, 7, 8}. 
? Calculate Value (Mean): 
Mean = (4 + 5 + 6 + 7 + 8)/5 = 6 
? Now we subtract the mean from each data set to obtain the 
deviation from the mean. 
Values 
Absolute Deviation from 
Mean 
|value – mean| 
4 2 
5 1 
6 0 
7 1 
8 2 
? Sum of Absolute Deviations: 
2 + 1 + 0 + 1 + 2 = 6 
? Mean Deviation: 
Mean Deviation = 6/5 = 1.2 
This gives the mean deviation of the given data set. 
Mean Deviation Formula 
There are various types of mean deviation formulas used depending upon the 
types of data given and the central point chosen for the given data set. We 
have different formulas for grouped data, and ungrouped data, also the mean 
deviation formula is different for deviation about mean and the deviation 
about median or mode. The image added below shows the mean deviation 
formula in various cases. 
 
Where, 
? ? – Summation 
? xi – Observations 
? µ  – Mean 
? n – Number of observations 
Mean Deviation Formula for Ungrouped Data 
For ungrouped data or data that is not properly arranged that is the given 
data is in raw form, the mean deviation is calculated using the formula, 
Mean Deviation = ?i = 1n |xi – x ¯ | / n 
 
 
where, 
? xi represents the ith observation 
? x ¯ represents any central point (mean, median, or  mode) 
? n represents the number of observations present in the data set 
Mean Deviation for Discrete Frequency Distribution 
In the discrete series, the data of each individual value is represented and 
their individual frequency is represented in the next column of the table. The 
table added below shows the data in a discrete frequency distribution table. 
Wages Number of Workers 
(Frequency) 
2500 7 
3000 9 
4000 5 
4500 6 
5000 3 
The formula  used to calculate the mean deviation in this type of data set is,