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When the mean is less than the median in a dataset, we say that the distribution of the data is left skewed.
This means there is a “tail” on the left side of the distribution:
Note: Sometimes a left skewed distribution is also referred to as a negatively skewed distribution.
In a left skewed distribution, the mean is less than the median:
What Causes the Mean to be Less than the Median?
A distribution is typically left skewed when it is uncommon for a variable to take on a small value and much more common for a variable to take on values concentrated around a larger value.
One real-life example of a left skewed distribution would be exam scores among students.
Most students might score between 70 and 90 on a particular exam and it’s extremely uncommon for many students to score near a zero.
When we create a histogram to visualize the distribution of exam scores for some class, it will naturally be left skewed:
The mean is naturally less than the median because the high frequency of values on the right side of the distribution causes the median value to be larger.
As a simple example, suppose we have the following dataset that contains the exam scores of 20 students in a class:
Dataset: 24, 45, 56, 71, 78, 80, 81, 81, 82, 83, 84, 85, 85, 89, 91, 91, 92, 93, 96, 97
Here are the mean and median values of this dataset:
- Mean: 79.2
- Median: 83.5
If we plot this distribution, it would be a left skewed histogram with most of the values concentrated on the right side of the histogram.
The following tutorials provide additional information about skewed distributions: