Skewness

Skewed Data

Data can be “skewed”, meaning it tends to have a long tail on one side or the other:

Negative Skew No Skew Positive Skew

 

Negative Skew?

Why is it called negative skew? Because the long “tail” is on the negative side of the peak.

People sometimes say it is “skewed to the left” (the long tail is on the left hand side)

The mean is also on the left of the peak.

The Normal Distribution has No Skew

A Normal Distribution is not skewed.

It is perfectly symmetrical.

And the Mean is exactly at the peak.

Positive Skew

And positive skew is when the long tail is on the positive side of the peak, and some people say it is “skewed to the right”.

The mean is on the right of the peak value.

 

 

Example: Income Distribution

Here is some data I extracted from a recent Census.

As you can see it is positively skewed … in fact the tail continues way past $100,000

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