# Mode (statistics)

Sebastian
For other uses, see Mode.

The mode is the value that appears most often in a set of data. The mode of a discrete probability distribution is the value xat which its probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled. The mode of a continuous probability distribution is the value x at which its probability density function has its maximum value, so the mode is at the peak.

Like the statistical mean and median, the mode is a way of expressing, in a single number, important information about arandom variable or a population. The numerical value of the mode is the same as that of the mean and median in a normal distribution, and it may be very different in highly skewed distributions.

The mode is not necessarily unique, since the probability mass function or probability density function may take the same maximum value at several points x1x2, etc. The most extreme case occurs in uniform distributions, where all values occur equally frequently. When a probability density function has multiple local maxima it is common to refer to all of the local maxima as modes of the distribution. Such a continuous distribution is called multimodal (as opposed to unimodal).

In symmetric unimodal distributions, such as the normal distribution, the mean (if defined), median and mode all coincide. For samples, if it is known that they are drawn from a symmetric distribution, the sample mean can be used as an estimate of the population mode.

## Mathematics, science, technology, and musicEdit

### In mathematicsEdit

• Range (mathematics), a set containing the output values produced by a function
• Interval (mathematics), also called range, a set of real numbers that includes all numbers between any two numbers in the set
• Range (statistics), the difference between the highest and the lowest values in a set
• Projective range, a line or a conic in projective geometry
• Column space, also called the range of a matrix, is the set of all possible linear combinations of the column vectors of the matrix
Plot the mean, median, mode, and range of the data shown on the line plot.  Grades 4 and up.
Pictograph Worksheets

Pictographs use symbols to show data.

Line Graph Worksheets

Line graphs (not to be confused with line plots) have plotted points connected by straight lines.

Pie Graph Worksheets

Pie graphs, or circle graphs, show percentages or fractions of a whole group.

Bar Graphs

Students can practice creating and interpreting bar graphs on these printable worksheets.