Mode

Topics: Measure of Central Tendency - Statistics

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(definition)

In a set of observations of a variable, the mode is the value that is repeated the most.

Mode only exists for quantitative variables.

Special Cases §

Every Value §

When every value is repeated the same amount of times, the mode doesn’t exist.

For example, the mode of $\left\{1,2,3,4,5\right\}$ doesn’t exist.

More Than One §

When two values are repeated the same amount of times and they are consecutive, the mode is the average of those two values.

For example, the mode of $\left\{3,4,4,5,5,6\right\}$ is $4.5$.

When two or more values are repeated the same amount of times and they are not consecutive, the mode is each of those values.

For example, the mode of $\left\{3,3,4,5,6,6\right\}$ is $3$ and $6$.

Random Variables §

(theorem)

Let $X$ be a random variable whose density function $f_X(x)$ we know.

We can find $X$’s mode by finding the local maximums of $f_X(x)$.