Measures of CENTRAL TENDENCY tells us about the “typical” or average value for a variable. In other words, measures of central tendency tell us how closely data in a variable group around some central point. This information can be used to make an initial prediction of the EXPECTED VALUE that a variable will take on.
Mode, Median, and Mean
There are three measures of central tendency:
- MODE — the value(s) that occurs most often (i.e., with greatest frequency) in a distribution of observations within a variable
- Most of the time, the mode corresponds to one value; sometimes, the mode corresponds to two (BIMODAL) or more (MULTIMODAL) values
- MEDIAN — the middle value when the observations within a variable are ranked in ascending order (i.e., from lowest to highest); in other words, the median is the observation with 50% of observations above and 50% of observations below it
- If there are an even number of observations, the median is equal to the sum of the two middle observations, divided by two
- MEAN — the arithmetic average of all the observations within a variable (i.e., the sum of values, divided by the number of values)
We cannot calculate all measures of central tendency on all levels of variables. Median requires rank ordering of values — which, in turn, requires that the variable has direction. Mean can only be calculated if values are associated with real numbers that have equal intervals of measurement between then. The HIERARCHY OF MEASUREMENT illustrates that any statistic that can be calculated for a lower level of measurement can be legitimately calculated and used for higher levels of measurement. Therefore:
- because mode can be calculated for nominal level variables, it can also be calculated on ordinal, interval, and ratio variables
- because median can be calculated for ordinal variables, it can also be calculated on interval and ratio variables
- because mean can be calculated for interval variables, it can also be calculated for ratio variables
| Measure | Description | Levels of Measurement |
|---|---|---|
| MODE | Value that occurs most often (i.e., with greatest frequency) of a variable | Nominal + Ordinal + Interval + Ratio |
| MEDIAN | Middle value when observations of a variable are ranked in ascending order | Ordinal + Interval + Ratio |
| MEAN | Average of all the observations of a variable | Interval + Ratio |
Mean vs. Median
Generally, we would opt for the mean over the median when either can be calculated on a particular variable. However, sometimes mean can be misleading when there are outliers in the data. An OUTLIER is an extreme value of a variable. When outliers are present, the mean is distorted: it will be skewed towards the outlier. In such situations, median may be a more precise measure of central tendency.