Classifying Data
Measures of Central Tendency and Dispersion
In addition to the levels of measurement, there are other simple statistical tools that are used in analyzing and interpreting data. These include the mode, median, and range. These are collectively known as the measures of central tendency.
| Levels of Measurement | Measures of Central Tendency | Measures of Dispersion |
|---|---|---|
| Nominal | Mode | Frequency of occurrence |
| Ordinal | Median | Frequency of occurrence |
| Interval | Mean | Variance/standard deviation |
| Ratio | Mean | Variance/standard deviation |
Mode
The mode is simply obtained by identifying the most frequent number occurring in a given set of numerical data. For example, if your academic grades in eight subjects are 85, 90, 87, 85, 91, 88, 85, and 85, then the mode is 85.
Median
The median is the middle value from a set of numerical data arranged from highest to lowest. If the numerical data are odd numbered, the one in the middle is the median. If the data are even numbered, the sum of the two values in the middle are divided into two to get the median. What do you think is the median in your academic grades?
Mean
The mean is the most powerful measure of central tendency. Its common name is average and is computed by dividing the sum (Σx ) with the number of cases or replicates ( n ). It can be represented by the equation: x = Σx/n, x with a bar on top as the symbol of the mean. The mean can represent the overall characteristic of a dependent variable. It can be used for nominal, ordinal, interval, and ratio data but is most appropriate for interval and ratio data.
