Average deviation

Average Deviation is a statistical term that refers to the average difference between each data point in a data set and the mean of that data set. It is a measure of dispersion in statistics, which quantifies how spread out the values in a data set are.

Definition

The average deviation, also known as the mean absolute deviation, is calculated by taking the sum of the absolute differences between each data point and the mean, and then dividing by the number of data points. The formula for average deviation is:

AD = Σ|X - μ| / N

where:

• AD is the average deviation,
• Σ denotes the sum of the values,
• |X - μ| is the absolute difference between each data point X and the mean μ, and
• N is the number of data points.

Usage

The average deviation is used in various fields such as statistics, finance, economics, and social sciences to measure the variability or dispersion in a set of data. It provides a numerical measure of the average distance of all data points from the mean, giving an idea of the spread of the data.

Comparison with Standard Deviation

While both average deviation and standard deviation are measures of dispersion, they are calculated differently and may give different results. The standard deviation squares the differences before averaging them, which gives more weight to extreme values. The average deviation, on the other hand, uses the absolute values of the differences, which gives equal weight to all values.

Limitations

One limitation of the average deviation is that it does not take into account the direction of the deviation. It only considers the magnitude of the deviation, not whether it is above or below the mean. This can lead to misleading results in certain situations.

See Also

• Mean
• Median
• Mode
• Range
• Variance
• Standard deviation