Descriptive Statistics: DEVIATION (4/5)

Deviation shows how the data deviates from the mean; the distance from the center point.

Deviation measures the difference between an observed value of an item in a dataset and some other value — usually it is the arithmetic mean (the simple average). The sign of deviation will determine its direction meaning that the positive deviation (+) exceeds the arithmetic mean and the negative deviation (-) subceeds the arithmetic mean.

The three most frequently used methods to measure deviation are:

1. VARIANCE

2. STANDARD DEVIATION

3. MEAN DEVIATION

1. Variance

What is variance? Variance measures how observations in a dataset differ from the arithmetic mean. What is the distance between items and the center of the dataset? Or, spread of data from the arithmetic mean.

How to calculate variance? Variance is the sum of the squared differences from the mean of each variable, divided by the total number of variables minus 1. It can be calculated using the following formula:

A. For a population variance:

σ2 = Σ(xi — x)2 / n

Where:

xi = Each value in the dataset

x = Arithmetic mean of all values in the dataset

n = Number of values in the dataset