A histogram is a type of chart that allows us to visualize the distribution of values in a dataset.
We say that a histogram is right skewed if it has a “tail” on the right side of the distribution:
Note: Sometimes a right skewed histogram is also referred to as a positively skewed histogram.
A right skewed histogram has the following two properties:
1. The peak of the distribution is on the left side.
2. The mean is greater than the median.
What Causes a Histogram to Be Right Skewed?
A histogram is typically right skewed when there is a limit on the minimum possible value but no limit on the maximum possible value.
The most obvious real-life example of a right skewed histogram would be the distribution of income in a country.
The minimum income that a person could earn is zero dollars while there is no maximum income that a person could earn.
In general, most individuals might earn around $40k per year but there will be a few outliers that earn several millions of dollars per year.
When we create a histogram to visualize the distribution of income, it will naturally be right skewed:
Why is the Mean Greater than the Median in a Right Skewed Histogram?
In a right skewed histogram, the mean is 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
Now suppose we have another dataset that contains the exact same incomes except the last value is now $2.5 million:
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 Difference Between Right Skewed & Left Skewed Histograms
The opposite of a right skewed histogram is a left skewed histogram.
This is a type of histogram that has a “tail” on the left side of the distribution:
This type of histogram has the following properties:
1. The peak of the distribution is on the right side.
2. The mean is less than the median.
Notice that these are the exact opposite properties of a right skewed histogram.
Read more about left skewed histograms in this tutorial.
Additional Resources
The following tutorials provide additional information about histograms:
How to Estimate the Mean and Median of Any Histogram
How to Estimate the Standard Deviation of Any Histogram
How to Describe the Shape of Histograms
