Mode

Frequency, not size

For $2,4,4,4,7,9$, the mode is $4$ because it appears three times. The mode is not the largest value and does not depend on numerical order.

Unlike mean and median, mode can summarize categories. If “bus” is the most common way students travel to school, bus is the modal category.

One, several, or no modes

A data set may be unimodal, bimodal, or multimodal. In $1,1,3,3,5$, both $1$ and $3$ are modes. If every value occurs equally often, many courses say the set has no mode because no value is more frequent than another.

State all values tied for greatest frequency rather than choosing one arbitrarily.

Frequency tables and graphs

In a frequency table, find the largest frequency and read its corresponding value or category. On a bar graph, the tallest bar identifies the mode.

Comparing centre measures

Mean uses every magnitude, median uses ordered position, and mode uses frequency. They can agree in a symmetric distribution, but they answer different questions.

In $1,2,2,3,12$, mode is $2$, median is $2$, and mean is $4$. The outlier pulls the mean but leaves mode and median unchanged.

Common mistakes

Choosing the largest number. Mode means most frequent, not greatest.

Reporting the frequency as the mode. Report the value or category attached to that frequency.

Forcing one mode. Include every tie for highest frequency.

Calculating a mean for category labels. Use mode for nominal data.

Quick self-check

• Which value or category has the greatest count?
• Is there a tie?
• Am I reporting the item rather than its frequency?
• Would frequency or percentage add important context?