About Mean Deviation
The deviation is a metric used in statistics and mathematics to find the difference between the observed and predicted value of a variable. The deviation is just the distance from the central point. Similarly, the mean deviation is used to determine how far values deviate from the data set's median.
Definition of Mean Deviation
The mean deviation is a statistical measure that is used to calculate the average deviation from a given data set's mean value. Using the procedure below, you can simply determine the mean deviation of the data values.
Step 1: Calculate the average of the data values.
Step 2: Subtract the mean value from each of the given data values (Note: Ignore the minus symbol)
Step 3: Now determine the average of the numbers from step 2.
Mean Deviation Formula
Below is the formula for calculating the mean deviation for the provided data set.
Mean Deviation = [Σ |X –µ|]/N
Here,
- Σ represents the addition of values
- X represents each value in the data set
- µ represents the mean of the data set
- N represents the number of data values
- | | represents absolute value, which ignores “-” symbol
Frequency Distribution Mean Deviation
To present it in a more compressed format, we group the data and highlight the frequency distribution of each group. These groups are known as class intervals. Grouping of data is possible in two ways:
- Frequency Distribution in Discrete Form
- Frequency Distribution in Continuous Time
Mean Deviation for Discrete Distribution Frequency
By discrete, we imply distinct or non-continuous, as term implies. Frequency (number of observations) supplied in set of data is discrete in nature in such a distribution.
Discrete distribution of frequency is a representation of data that consists of values x1,x2, x3.........xn, each occurring with a frequency of f1, f2,... fn, correspondingly.
To calculate mean deviation for grouped data and particularly for discrete distribution data following steps are followed:
Step I: Determine measure of central tendency from which the mean deviation will be calculated. Allow this to be a.
If this measure is mean then it is calculated as,
where
If the measure is median, the given set of data is arranged in ascending order, the cumulative frequency is calculated, and the observations whose cumulative frequency is equal to or just greater than N/2 are taken as the median for the given discrete frequency distribution, and this value is seen to be in the middle of the distribution.
- Step 2: Using the measure of central tendency established in step 1, calculate the absolute deviation of each observation (I)
- Step III: Using the formula, calculate the mean absolute deviation around the measure of central tendency.
If the central tendency is mean then,
In case of median
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