Mean Deviation
Mean deviation measures the deviation of the observations from the mean of the distribution.
Since the average is the central value of the data, some deviations might be positive and some might be negative. If they are added like that, their sum will not reveal much as they tend to cancel each other’s effect.
For example :
Let us consider this set of data : -5, 10, 25
Mean = (-5 + 10 + 25)/3 = 10
Now a deviation from the mean for different values is,
- (-5 -10) = -15
- (10 – 10) = 0
- (25 – 10) = 15
Now adding the deviations, shows that there is zero deviation from the mean which is incorrect. Thus, to counter this problem only the absolute values of the difference are taken while calculating the mean deviation.
Mean Deviation Formula :
MD =
Mean Deviation for Ungrouped Data
For calculating the mean deviation for ungrouped data, the following steps must be followed:
Step 1: Calculate the arithmetic mean for all the values of the dataset.
Step 2: Calculate the difference between each value of the dataset and the mean. Only absolute values of the differences will be considered. |d|
Step 3: Calculate the arithmetic mean of these deviations using the formula,
M.D =
This can be explained using the example.
Example: Calculate the mean deviation for the given ungrouped data, 2, 4, 6, 8, 10
Solution:
Mean(μ) = (2+4+6+8+10)/(5)
μ = 6
M. D =
⇒ M.D =
⇒ M.D = (4+2+0+2+4)/(5)
⇒ M.D = 12/5 = 2.4
Read More On :
Measures of Dispersion | Types, Formula and Examples
Measures of Dispersion are used to represent the scattering of data. These are the numbers that show the various aspects of the data spread across various parameters.
Let’s learn about the measure of dispersion in statistics , its types, formulas, and examples in detail.
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