Average Calculator

Calculate Average Calculator

How to Work Out an Average

An average is a single number that represents the centre or typical value of a set of data. In everyday life we calculate averages constantly: average exam scores, average temperatures, average journey times, average salaries. The most common type of average is the arithmetic mean, usually just called "the average".

The Mean Formula

The arithmetic mean is calculated using this formula:

Example: You want to find the average of five test scores: 55, 62, 70, 78 and 85.

1. Add all values: 55 + 62 + 70 + 78 + 85 = 350
2. Count the values: There are 5 scores
3. Divide: 350 ÷ 5 = 70

The mean average test score is 70. You can verify this using the calculator above by entering: 55, 62, 70, 78, 85.

Types of Averages: Mean, Median and Mode

There are three main types of average used in statistics and everyday calculations. Each has different strengths depending on the data set.

Arithmetic Mean

The arithmetic mean is the standard "average" taught in UK schools at KS3 and above. Add all values, divide by the count. It works perfectly when data is roughly symmetrical and there are no extreme outliers. For a class of 30 students taking the same exam, the mean score is the most useful summary statistic.

Median

The median is the middle value when you sort a list from smallest to largest. If there is an even number of values, the median is the mean of the two middle values.

Example: Sorted data: 10, 15, 20, 25, 30. The median is 20 (the third value out of five).

The median is far more useful than the mean for income and house prices. UK median annual pay is around £35,000, but the mean is pulled upward to around £42,000 by high earners. The Office for National Statistics (ONS) uses median figures to represent "typical" earnings for this reason.

Mode

The mode is the value that appears most often in a data set. A data set can have no mode (all values are different), one mode, or multiple modes (bimodal, trimodal, etc.).

Example: Data: 3, 5, 5, 7, 9, 9, 9, 11. The mode is 9 (appears 3 times).

The mode is most useful for categorical or discrete data. A shoe retailer wants to know which shoe size to stock most — that is the mode, not the mean.

Geometric Mean

The geometric mean is calculated by multiplying all values together and taking the n-th root, where n is the count of values. It is the correct average to use for growth rates and investment returns because it accounts for compounding.

Example: Annual returns of 10%, 20% and -5%. Geometric mean = (1.10 × 1.20 × 0.95)^(1/3) − 1 = 7.84% per year. The arithmetic mean would give a misleadingly high 8.33%.

How to Calculate a Weighted Average

A weighted average assigns different levels of importance (weights) to different values. It is widely used in education, finance and statistics.

University Grade Example

Suppose your university degree has these components:

Note that a simple (unweighted) mean of the three scores would be (68+72+58) ÷ 3 = 66%, which does not reflect that the final exam counts for half the grade. The weighted average of 64.2% is the correct figure.

Weighted Average for Investments

Investors use weighted averages to calculate portfolio returns. If you hold £10,000 in Fund A (returning 8%) and £40,000 in Fund B (returning 5%), your portfolio return is not simply (8+5) ÷ 2 = 6.5%. The weighted average return is: (10,000 × 8% + 40,000 × 5%) ÷ 50,000 = (800 + 2,000) ÷ 50,000 = 5.6%.

When to Use Each Type of Average

Choosing the right type of average matters. Using the wrong one can be misleading or factually incorrect. Here is a practical guide:

Use the Mean When:

• The data is roughly symmetrically distributed (not heavily skewed)
• There are no extreme outliers that would distort the result
• You need to use the average in further calculations (e.g., standard deviation requires the mean)
• Examples: exam scores, heights, temperatures, reaction times

Use the Median When:

• The data is skewed or contains outliers
• You want to represent the "typical" individual rather than the mathematical centre
• Examples: household income, house prices, waiting times in A&E, salary surveys
• The ONS, ONS ASHE, and most government statistical releases use median for income data

Use the Mode When:

• The data is categorical or discrete
• You want to find the most common or popular item
• Examples: most popular car colour, most common shoe size, most frequent response in a survey

Use the Geometric Mean When:

• Calculating average growth rates, investment returns or compound changes over time
• Values are multiplicative rather than additive in nature
• Examples: average annual return on an investment, average population growth rate

UK Average Salary — Why Median Matters

The UK median annual salary for full-time employees is approximately £35,000 according to the ONS Annual Survey of Hours and Earnings (ASHE) 2024. This is the figure most commonly quoted in the press and used for policy decisions.

However, the mean (arithmetic average) salary is significantly higher at around £42,000. This is because a small number of very high earners (executives, bankers, footballers) pull the mean upward. The median is a more honest representation of what a "typical" UK worker earns.

This illustrates why knowing which type of average is being quoted matters enormously. When a newspaper headline says "average salary rises to £42,000", it may be reporting the mean rather than the median, which paints a rosier picture than most workers experience.

How to Calculate Average in Excel

Microsoft Excel provides built-in functions for every type of average. These are essential for anyone working with data in spreadsheets.

Weighted Average in Excel

Excel does not have a built-in WEIGHTEDAVERAGE function. To calculate a weighted average in Excel, use SUMPRODUCT divided by SUM:

Where column A contains the values and column B contains the weights. This formula multiplies each value by its weight, sums the products, and divides by the total weight.