Central tendency can be defined as measures of the location of the middle in a distribution.
The most common types of central tendency are:
| Mean | The average value |
| Median | The value in the absolute middle |
| Mode | The most frequently occurring value |
Mean
The mean is perhaps the most commonly used type of central tendency and we get it by dividing the sum of all values by the number of observations.
| Example |
 | | | |
| 1.1 kilos | 0.8 kilos | 1.1 kilos | 1.0 kilos |
| Let us assume that we have four fish of different weight (see the picture above). What is the mean? First, we add the values together: 1.1+0.8+1.1+1.0=4.0 Then we divide the sum of the values by the number of fishes: 4.0/4=1. The mean is thus 1 kilo. |
Median
The median – i.e. the value in the absolute middle of the distribution – is obtained by sorting all the observations’ values from low to high and then identifying the value in the middle of the list.
| Example |
 | | | | | | | | |
| 158 cm | 159 cm | 164 cm | 165 cm | 173 cm | 174 cm | 175 cm | 179 cm | 181 cm |
| Let us assume that we have nine individuals of different height (see the picture above). After we have sorted them so that the shortest one is to the left and the tallest one is to the right, we can locate the value in the middle of the distribution. The median is thus 173 cm. |
| Note When we have an odd number of values, it is easy to identify the value in the absolute middle of the distribution. When we have an even number of values, we get the median by adding the two values in the middle together and dividing the sum by 2. |
Mode
The mode – or type – is defined as the most frequently occurring value in a distribution. Here as well, one starts by sorting observations from the lowest to the highest value and then identifies the most common value.
| Example |
 | | | | | | |
| Household 1 | Household 2 | Household 3 | Household 4 | Household 5 | Household 6 | Household 7 |
| 1 car | 1 car | 1 car | 1 car | 2 cars | 2 cars | 3 cars |
| Let us assume that we have information about the number of cars in each of seven households (see the figure above). There are four households with one car, two households with two cars, and one household with three cars. The mode is thus 1 car. |
How to choose between mean, median, and mode?
The choice of type of central tendency is based on:
- The measurement scale of the variable.
- The distribution of the variable.
Generally, if the variable is categorical (nominal or ordinal), the mode is preferred.
If the variable is continuous (ratio or interval), the mean or the median is preferred. The mean is chosen if the variable is normally distributed and the median is chosen if the variable has a skewed distribution.
Why should one not use the median or the mean for categorical variables?
For nominal variables, it is easy to give an answer. Let us take country of birth as an example. In this example, the variable is coded into four categories: 1) Sweden, 2) China, 3) Canada, and 4) Norway. This is clearly a nominal variable. Since the order of the categories is random (i.e. the order of the categories does not really matter), the location of the absolute middle in the distribution would not tell us anything information about the variable: the “content” of the middle would change completely if we changed the order of the categories. Let us take gender (which is also on a nominal scale) as another example: it would not make any sense to give the mean or median of gender.
For ordinal variables, however, the median (or even the mean) is sometimes used. For example, if we have five categories of occupational class, which can be ranked from lower class to upper class, it may be interesting to give the value of the median (for example, in this case, the median could be lower non-manuals which would tell us something about the distribution of values). This strategy is even more common for ordinal variables that based on scales. For example, if we ask someone about their attitudes toward the government, and the response options range from very negative to very positive, the median (or the mean) could provide relevant information.
Why is it important to consider the distribution of the variable for continuous variables before we decide on the type of central tendency?
If we take a look at the figures below, we can draw the following conclusions: if we have a perfectly normally distributed variable, the mean, median and mode would all be the same. However, if the distribution is skewed, the median would be a better description of the location of the middle in the distribution.
