The mode in this visualization
The mode of a set of data is the value that occurs most often. How often a value occurs is its frequency, so the mode is the value with the greatest frequency; when several values share it, each of them is a mode. Here each value has a stack of dots, one for each time it occurs, and the mode is the value under the tallest stack. You build the data yourself, as numbers from 0 to 10 or as students’ answers to how they get to school.
The mode is a value, not a count. If 3 occurs six times and nothing occurs more often, the mode is 3; six is its frequency. The readout gives that frequency out of the whole, because the most common value need not be common: it can make up well under half of the data and still be the mode.
Finding the mode takes only counting. Nothing is added and nothing has to be put in order, so data that are names rather than numbers have a mode too. Ways of getting to school have no natural order and can’t be added, so they have no mean or median, but they do have a mode. Categories with an order, such as low, medium and high, have a median as well.
Ties, and when nothing stands out
Data with two modes are called bimodal, and with more, multimodal. That is an ordinary case, not a broken one: every mode is reported, without averaging them or choosing one. When every value in the data occurs equally often, the definition makes each of them a mode, and the mode then singles out nothing. Many books, and some standard references, say instead that data in which no value repeats have no mode. This page follows the definition and lists them all. With no data at all there is nothing to count and no mode.
Mode, median and mean
They are three different summaries of the same numbers. The mode is the most common value, the median is the middle value once the data are in order, or halfway between the two middle values when there is an even number of them, and the mean is the sum divided by how many values there are. When the data are symmetric and have a single mode, the three are equal. A long tail to one side can pull them apart: a few large values pull the mean towards them, the median moves less, and the mode stays with the tallest stack.
The mode responds only to counts. When one stack is well ahead, adding a value here and there leaves the mode where it is. When the two tallest stacks differ by one, one more value for the shorter makes a tie, and one more again moves the mode to it, however far along the axis it lies.
Things to notice
- Measurements such as heights rarely repeat exactly, so the mode of the raw values often says little. Grouped into intervals of equal width, the data make a histogram, and its tallest bar marks the modal class: the interval where the values are most crowded. It is an interval, not the mode itself, and it can move when the intervals are chosen differently.
Controls
- Click a column at some height to give that value that many dots; drag across to set several columns, or along below the axis to empty them.
- With the keyboard, Tab to the stacks: the up and down arrows change how many times a value occurs, the left and right arrows move to the next value.