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When the mean is greater than the median in a dataset, we say that the distribution of the data is right skewed.
This means there is a “tail” on the right side of the distribution:
Note: Sometimes a right skewed distribution is also referred to as a positively skewed distribution.
In a right skewed distribution, the mean is greater than the median:
What Causes the Mean to be Greater than the Median?
A distribution is typically right skewed when there is a limit on the minimum possible value but no limit on the maximum possible value.
One real-life example of a right skewed distribution is the distribution of income in a country.
The minimum income that a person could earn is zero dollars but there is no maximum income that a person could earn.
When we create a histogram to visualize the distribution of income, it will naturally be right skewed:
The mean is naturally greater than the median because the large values on the right “tail” of the distribution will greatly inflate the value of the mean.
As a simple example, suppose we have the following dataset that contains the income of 10 individuals:
Dataset 1: $30k, $35k, $35k, $40k, $50k, $55k, $55k, $70k, $90k, $110k
Here are the mean and median values of this dataset:
- Mean: $57k
- Median: $52.5k
Dataset 2: $30k, $35k, $35k, $40k, $50k, $55k, $55k, $70k, $90k, $2.5 million
Here are the mean and median values of this dataset:
- Mean: $296k
- Median: $52.5k
This last outlier value causes the mean income to increase significantly.
And if we plot this distribution, it would be a right skewed histogram with the $2.5 million value located on the right “tail” of the histogram.
The following tutorials provide additional information about skewed distributions: