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?

Graph of negative skew showing mean, median, and mode lines with the tail on the left

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

Some people say it is skewed left, meaning the long tail is on the left hand side

In a negative skew, the measures of central tendency are pulled in different directions:

The Mode is at the highest peak
The Median is left of the peak
The Mean is pulled furthest left by the long tail

So: Mean < Median < Mode

The Normal Distribution has No Skew

Symmetrical normal distribution curve with mean, median, and mode aligned at the center peak
A Normal Distribution isn't skewed.
It is perfectly symmetrical.
And the Mean is exactly at the peak.

Positive Skew

Graph of positive skew showing mode, median, and mean lines with the tail on the right

And positive skew is when the long tail is on the positive side of the peak

Some people say it is "skewed right".

The mean is on the right of the peak value.

Example: Income Distribution

Bar chart of household income showing a strong positive skew with a long tail to the right

Here's some data extracted from a recent Census.

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

Quick Question: A bakery usually sells 10 to 15 cakes a day. But on a few holiday days they sell over 100 cakes. Is this data skewed left (negative) or right (positive)?

Answer: It is skewed right (positive skew), because the rare high-sales days create a long tail on the positive (right) side of the graph.

Calculating Skewness

"Skewness" (the amount of skew) can be calculated, for example you could use the SKEW() function in Excel or OpenOffice Calc.

8775, 8776, 8777, 8778, 8779, 8780, 8781, 8782, 8783, 8784