Let’s Summarize

We have two different measurements for determining the center of a distribution: mean and median. When we use the term center, we mean a typical value that can represent the distribution of data.
The mean is the average. We calculate the mean by adding the data values and dividing by the number of individual data points.
The mean has the following properties:
- It is the fair-share measure. For example, imagine that you have 10 homework scores. Say that your scores vary, but the mean is 84. Then you have 84(10) = 840 points, which is like having an 84 on each of the 10 assignments.
- The mean is also referred to as the balancing point of a distribution. If we measure the distance between each data point and the mean, the distances are balanced on each side of the mean.
The median divides the distribution in half. It has the same number of data points above it as below it.
General Guidelines for Choosing a Measure of Center
- Always plot the data. We need to use a graph to determine the shape of the distribution. By looking at the shape, we can determine which measures of center best describe the data.
- Use the mean as a measure of center only for distributions that are reasonably symmetric with a central peak. When outliers are present, the mean is not a good choice.
- Use the median as a measure of center for all other cases.

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