A measure of centre describes a typical value. A measure of spread describes how widely the values vary. Compare like quantities in the same units.
| Measure | Meaning |
|---|---|
| Mean, \(\overline{x}\) | \(\overline{x}=\dfrac{\text{sum of the values}}{\text{number of values}}\) |
| Median | The middle value after ordering the data; for an even number of values, average the two middle values. |
| Mode | The value with the greatest frequency; there may be more than one mode or no mode. |
| Range | Largest value minus smallest value. |
| Standard deviation, \(\sigma\) | A smaller standard deviation means less spread about the mean. It has the same unit as the data. |
For a complete data set of \(n\) values, use the population standard deviation: \(\sigma=\sqrt{\dfrac{\sum x^2}{n}-\overline{x}^{\,2}}\).
Enter each observation in the calculator statistics list. For a frequency table, enter the values and their frequencies in separate columns. Check that the calculator total \(n\) equals the number of observations, then read the population result \(\sigma_x\), not the sample result \(s_x\).
Adding or subtracting the same number from every observation changes the mean by that number but leaves the standard deviation unchanged: the distances from the mean stay the same.
Keep unrounded calculator values during working. Round only the final answer to the accuracy requested. A larger mean is not automatically better: decide what the measured quantity represents.
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