Describes an entire set of observations with a single value representing the center of the data. The mean (arithmetic average) is the sum of all the observations divided by the number of observations. For example, the waiting time (in minutes) of five customers in a bank are: 3, 2, 4, 1, and 2. The mean waiting time is:
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3 + 2 + 4 + 1 + 2 5 |
= 12 5 |
= 2.4 min |
On average, a customer waits 2.4 minutes for service at the bank.
Because the mean depends equally on all of the data including extreme values, it may not be representative of the center for skewed data.
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Symmetric data: the mean (pink line) lies near the center of the distribution, making it a good representation of the center. |
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Skewed data: the mean (pink line) is pulled in the direction of the heavier tail, making it misleading as a representation of the center. |
Many statistical analyses use the mean as a standard reference point.
m represents the population mean; X (or m hat) represents the sample mean.
