Below is a normally distributed set of 21 observations, each observation represented by a red dot. What is the mean of this distribution?
By plugging our data points into the formula for the sample mean, we find that the mean of this distribution is 5.
As we expect, the calculated mean is at the distribution's peak, in the center of the symmetric distribution, equal to the median and the mode. Each value to the right of 5 has an equidistant value on the left side of the distribution.
What if we look at a skewed distribution?
In this distribution, we can clearly see that there are now data points to the more extreme right of the distribution's peak. It follows that the median of the distribution is to the right of the mode, and the mean is to the right of both the mode and the median.
On this plot, the mode of the distribution is 3, the median is 4, and the calculated mean is 4.67.
On the following screen, you will be able to create your own plots and explore where the mean falls when distributions take on different shapes.
| Mean = | |
| Median = | |
| Mode = |