Mean, Median, and Mode
By Elisabetta Tola / 3 minute read
Often, when trying to convey the meaning of the data, we use representative descriptive characteristics like mean, median, and mode. Any of the three is sometimes referred to as the average, though most of the time “average” is associated with “mean.”
Imagine you have an airplane full of passengers and you measure the height of each individual. If you were to plot that information on a graph, you would probably see a few dots on the low end, a few dots on the high end, and a bunch of dots clustered together in the middle. That is your standard bell curve, also called a “normal distribution.” In this case, the mean, median, and mode tend to be similar, if not coincident, at the midpoint of the graph.
Biological features, like height and weight, usually behave like that. To calculate the mean, you simply sum up all of the values in your data set and divide it by the number of entities. If the sample is big enough, the values are likely to distribute in that symmetrical shape around the mean.
Associated with mean is “standard deviation.” This term refers to how far the data points are, on average, from the mean. In other words, is the bell skinny (the data are clustered close together)? Or fat (the data are spread apart)? Small standard deviations suggest more-uniform data.
However, in a small sample, even biological features might be distributed in a non-normal way. For instance, what if a professional basketball team happened to be on board our imaginary flight? The presence of such tall outliers would affect the distribution of the values. Now our bell curve has a bump on the right, and the mean shifts to the right.
In such cases, it can be better to use the median, which is the middle number of all our values, if we arrange them from smallest to largest.
You often see “median” used to talk about income, especially in populations with high inequality. The presence of a few multibillionaires would shift the mean well above the level of income ever experienced by most citizens. So the median does a better job of indicating the midpoint on a distribution: half of the people make more than the median, half make less.
Another way to describe data is through the mode, which provides the value that is most common or most frequently occurring. As an example, let’s disembark from our imaginary plane and instead head to the highways.
In 2018, according to the National Highway Traffic Safety Administration, here was the distribution of fatal accidents by time of day:
| Midnight-3:59 am | 4,574 |
| 4:00-7:59 am | 4,388 |
| 8:00-11:59 am | 4,154 |
| Noon-3:59 pm | 5,943 |
| 4:00-7:59 pm | 7,329 |
| 8:00-11:59 pm | 7,022 |
If we had the exact time for each accident, you could calculate a mean time of the accidents — it would be sometime in the early afternoon. Likewise, you could also determine a median time, which would also be in the early afternoon. However, neither would really tell you much in terms of the times of day that public-safety officials should aim at in order to reduce fatal accidents. The most common times — or the mode — for fatal accidents, is in the evening.
Therefore, from a public-safety point of view, officials should focus on improving safety in the evening — maybe through enforcement, lighting, signage, or road markings — in order to have the biggest impact on fatal accidents.
Some data sets don’t have single modes. There might be two points that feature the most frequent data. That is known as bimodal distribution. (More than two modes would be called “multimodal distribution.”)
An example of this is with the most common ages of drivers involved in fatal accidents. New, young drivers and old drivers far outstrip drivers between the ages of 24 and 65 in terms of accidents. Therefore, policies aimed at reducing fatal accidents might focus on addressing those two age groups.