# Mean, Median and Mode

This video will define mean, median and mode for you. It will go over how to find each using a set of data. For more help, check out our Mean, Median and Mode Lessons Page

Credit goes to TheAnimatedClassroom

### What Are Mean, Median, and Mode?

In statistics, mean, median, and mode are measures of central tendency, which aim to describe the center or typical value of a dataset. Each measure serves a unique purpose and provides different insights into the distribution of the data.

Mean

The mean, also known as the average, is calculated by adding up all the values in a dataset and then dividing by the total number of values. Mathematically, the mean (μ) of n values x1, x2, …, xn is computed as:

In simpler terms, it’s the sum of all values divided by the number of values. The mean is sensitive to extreme values, also known as outliers, because it takes into account every value in the dataset.

For example, consider the dataset {1, 2, 3, 4, 100}. The mean is:

Here, the outlier (100) significantly influences the mean, pulling it towards higher values.

The mean is influenced by outliers and provides a measure of central tendency based on the sum of all values.

Median

The median is the middle value of a dataset when it is ordered from least to greatest. If the dataset has an odd number of values, the median is simply the middle value. If the dataset has an even number of values, the median is the average of the two middle values.

For example, in the dataset {3, 6, 9, 12, 15}, the median is 9. In the dataset {2, 4, 6, 8},

the median is (4 + 6) / 2 = 5.

Unlike the mean, the median is not affected by extreme values or outliers. It simply represents the value that splits the dataset into two equal halves.

The median is not affected by outliers and represents the middle value of the ordered dataset.

Mode

The mode is the value that appears most frequently in a dataset. A dataset can have one mode (unimodal), two modes (bimodal), or more than two modes (multimodal). It’s possible for a dataset to have no mode if all values appear with the same frequency.

For example, in the dataset {2, 4, 4, 6, 6, 6, 8, 8, 8, 8}, the mode is 8 because it appears most frequently.

The mode is useful for categorical data or discrete data with a relatively small number of unique values. Unlike the mean and median, the mode can be applied to both numerical and categorical data.

The mode identifies the most common value(s) in the dataset and is independent of outliers.