EDEXCEL GCSE FOUNDATION MATHS - What are Averages and Range

Averages and Range

An average is a single number that represents a typical value for a set of data. It gives us an idea of the central value of the data.

There are three main types of averages:

Mean: This is the most common type of average. To calculate the mean, you add up all the values in the dataset and then divide by the number of values.
Median: This is the middle value in a set of data when the values are arranged in order. If there are two middle values, the median is the average of those two values.
Mode: This is the value that appears most often in a set of data. There can be multiple modes in a dataset.

Example:

Find the mean of the following numbers: 5, 8, 12, 10, 7

Steps:

Therefore, the mean of the numbers is 8.4.

The range is a measure of spread in a dataset. It tells us the difference between the highest and lowest values in the set.

Example:

Find the range of the following numbers: 2, 15, 7, 1, 10

Steps:

Identify the highest and lowest values: Highest value is 15, lowest value is 1.
Subtract the lowest value from the highest value: 15 - 1 = 14

Therefore, the range of the numbers is 14.

Scenario: Two classes, Class A and Class B, took a test. Here are their scores:

Class A: 60, 75, 80, 85, 90

Class B: 70, 75, 80, 85, 95

Calculations:

Interpretation:

Class B has a higher average score than Class A, indicating better overall performance.
Class A has a wider range of scores than Class B, indicating more variability in performance within the class.

Averages and Range are useful tools for summarizing and comparing data.
The mean is the most common type of average.
The range provides information about the spread of the data.
It's important to choose the right average and measure of spread for the specific data you are working with.