Calculate Mean Deviation From Mean for The Following Data

The mean deviation from the mean is a measure of statistical dispersion that calculates the average distance between each data point and the mean of the data set. It provides insight into how spread out the values are around the central tendency.

What is Mean Deviation from Mean?

The mean deviation from the mean is a measure of statistical dispersion that calculates the average absolute difference between each data point and the mean of the data set. Unlike standard deviation, which uses squared differences, mean deviation uses absolute differences, making it less sensitive to extreme values.

This measure is particularly useful when you want to understand the typical distance of data points from the mean without being affected by outliers in the same way that variance or standard deviation might be.

How to Calculate Mean Deviation from Mean

To calculate the mean deviation from the mean, follow these steps:

Calculate the mean (average) of your data set.
For each data point, find the absolute difference between the data point and the mean.
Sum all these absolute differences.
Divide the sum by the number of data points to get the mean deviation.

This process gives you a measure of how spread out the data points are from the mean.

Formula for Mean Deviation from Mean

Mean Deviation Formula

Mean Deviation (MD) = (Σ |xᵢ - x̄|) / n

Where:

xᵢ = each individual data point
x̄ = mean of the data set
n = number of data points
| | = absolute value

The formula calculates the average absolute deviation of each data point from the mean. The result is in the same units as the original data.

Worked Example

Let's calculate the mean deviation for the following data set: 10, 12, 14, 16, 18.

Calculate the mean: (10 + 12 + 14 + 16 + 18) / 5 = 14
Find absolute differences from the mean:
- |10 - 14| = 4
- |12 - 14| = 2
- |14 - 14| = 0
- |16 - 14| = 2
- |18 - 14| = 4
Sum of absolute differences: 4 + 2 + 0 + 2 + 4 = 12
Mean deviation: 12 / 5 = 2.4

The mean deviation from the mean for this data set is 2.4.

Interpreting the Result

A higher mean deviation indicates that the data points are more spread out from the mean, while a lower mean deviation suggests that the data points are closer to the mean. This measure is particularly useful when comparing the dispersion of different data sets.

For example, if you have two data sets with the same mean but different mean deviations, the set with the higher mean deviation will have more variability in its values.

FAQ

What is the difference between mean deviation and standard deviation?: Mean deviation uses absolute differences, while standard deviation uses squared differences. This makes mean deviation less sensitive to outliers.
When should I use mean deviation instead of standard deviation?: Use mean deviation when you want a measure of dispersion that is not affected by extreme values or when you need a simpler, more intuitive measure of spread.
Can mean deviation be negative?: No, mean deviation is always non-negative because it uses absolute differences.
Is mean deviation affected by outliers?: Mean deviation is less affected by outliers than standard deviation because it doesn't square the differences.
How does mean deviation compare to the range?: Mean deviation provides a more detailed measure of spread than the range, as it considers all data points rather than just the minimum and maximum values.