In mathematics, an 'average' is a single number that represents the central or typical value within a set of numbers. It gives us a summary of the data.

While we often use the word 'average' to mean one specific thing, there are actually three main types of averages used in statistics:

1. Mean: The sum of all values divided by the number of values.

2. Median: The middle value when the numbers are arranged in order.

3. Mode: The value that appears most frequently in the set.

The mean is the most common type of average. It is calculated by adding up all the numbers in a dataset and then dividing by how many numbers there are.

Formula: Mean = (Sum of all values) / (Number of values)

The mean is useful because it includes every value in the dataset in its calculation, but it can be sensitive to outliers (extremely high or low values).

The median is the value that is physically in the middle of a dataset when the numbers are sorted from least to greatest.

If there is an odd number of values: The median is the middle number.

If there is an even number of values: The median is the mean of the two middle numbers.

The median is very useful because it is not affected by unusually high or low values (outliers).

The mode is the simplest average to find. It is the number that appears most often in a dataset.

A dataset can have one mode, more than one mode (bimodal, trimodal, etc.), or no mode at all if every number appears only once.

The mode is most useful for categorical data (like 'most popular car color') but can be used for numerical data as well.

Averages are used constantly to understand performance and trends.

Your Grade Point Average (Mean) is calculated by summing your grades and dividing by the number of classes.

If a teacher wants to know the score that separates the top 50% of students from the bottom 50%, they would find the Median test score.

If a shoe store wants to know which shoe size to stock the most of, they would find the Mode of shoe sizes sold.