# Averages

Source: https://projectgcse.co.uk/maths/algebra/averages

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The average of a set of numbers is the value which best represents it. There are three different types of averages.

**Mean**
This is also known as the arithmetic mean. It is found by dividing the sum of the set of numbers with the actual number of values.
For example: Find the mean of 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.
Sum of values: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
Number of values = 10
Mean of values = 55 / 10 = 5.5

**Median**
The median of a set of numbers is the middle number when the numbers are put in order, from the lowest value to the highest value. The median can be thought of as the ( (Number of Values) + 1 ) / 2 ) th value.
For example: Find the median of 2, 4, 8, 7, 4, 6, 10, 8, and 5.
In order: 2, 4, 4, 5, 6, 7, 8, 8, 10
Middle value = ( ( 9 + 1 ) / 2 ) th value = 5 th value
Middle value = 2, 4, 4, 5, 6, 7, 8, 8, 10
Median = 6

**Mode**
The mode is the value which occurs most frequently in the set of values. The mode of the set of values is also known as the modal value.
For example: Find the mode of 1, 2, 2, 3, 4, 4, 5, 5, 5, 5, 7, 8, 8 and 9.
Modal value = 5