Mode

This tutorial covers how to interpret and calculate the mode of a dataset. You'll learn about:

1. Mode
2. Qualitative Sets
3. Distributions

1. Mode

Suppose that you have the heights of the Chicago Bulls basketball team in this list:

Using this list, can you find out what height would be considered typical for this team?

There's a couple of different ways we can go about answering that question.

1. You could find the mean, which would be add all these numbers up and divide by 15.
2. You could order them least to greatest and find the number that's in the middle. That would be the median.
3. You can look at the values that appear most frequently, which would be the mode.

• Mode
• The most frequently appearing number in a set of quantitative data or most frequently occurring category in a set of qualitative data.

In a quantitative data set like you have in this example, the mode is the most frequently occurring number or numbers, assuming that they occur more than once.

In our dataset of heights,you can see that 81 occurs four times and 79 occurs four times. Unlike with means and medians, a distribution can have more than one mode. In this case, 79 and 81 are both modes.

Suppose a class has 12 students. Here are the grades from a 10-point quiz are listed here. Determine the mode.

You probably realize that the mode is nine: It appears four times, and nothing else appears more than three times.

2. Qualitative Sets

You can also find the mode of a qualitative dataset. In a qualitative dataset, the mode is the most frequently occurring category or the largest category.

Here, there are several large categories, but the largest category is the red: biology. So biology would be the mode of this dataset.

3. Distributions

In a distribution that is fully graphed out, you might have something that's multi-peaked.

As this graph shows, there is a gape between the two highest peaks, where the amounts decrease very precipitously and then rise again.

In a distribution, we would call both of these areas modes. The values near five and near eight would both be considered modes because they are the different peaks in the distribution. It might still be called bimodal, although in reality there is only the one mode, at eight. There is only one highest bar, however, we might still call this distribution bimodal.

The mode is the most common value in a dataset. In qualitative datasets, that value can be a category, in a quantitative dataset, the value will be a number. There can be one mode, many modes if several values appear an equal amount of plural times, or no mode if no value appears more than one time.

Modes may also refer to the peak or peaks of distributions, even if they're not the tallest point in the distribution. If a distribution has many peaks, we might call them bimodal or multimodal.

Thank you and good luck!