Mean definition
The mean is a type of average used to describe a set of numbers with one representative value. To find the mean, add all the values together and then divide by the number of values. For example, for the numbers 4, 6, 8 and 10, the total is 28 and there are 4 values. The mean is 28 divided by 4, which equals 7.
The mean is sometimes called the arithmetic mean. It is useful because it uses every value in the data set. If one value changes, the mean may change too. This makes it sensitive to the whole data set, which can be helpful when the values are fairly balanced. However, it can also be affected strongly by unusually large or unusually small values called outliers.
Mean is used in statistics, data handling, probability, science, geography, business, sport, finance and real-life decision making. At GCSE level, students calculate the mean from a list of values, from tables and from frequency tables. They may also compare means between two sets of data or explain why the mean might not be the best average for a particular situation.
The basic formula is mean = total of values divided by number of values. For example, if five students score 12, 15, 18, 20 and 25 marks, the total is 90. There are 5 students, so the mean score is 90 divided by 5, which equals 18. This means 18 is the average score using the mean method.
The mean can also be calculated from a frequency table. If a table shows values and how often they occur, multiply each value by its frequency, add those products, and divide by the total frequency. For example, if the value 3 occurs 4 times, it contributes 12 to the total. This method is important because raw data is often summarised in tables rather than written as a long list.
Outliers can make the mean misleading. For example, the numbers 5, 6, 7, 8 and 100 have a mean of 25.2, but most of the values are much smaller than this. The outlier 100 pulls the mean upwards. In this situation, the median might give a better idea of a typical value. This is why students should understand not only how to calculate the mean, but also when it is appropriate to use it.
Mean is useful in real life for finding average test scores, average temperatures, average wages, average sales, average speed and average costs. Businesses use means to track performance, schools use them to review results, and scientists use them to summarise experiment data. The mean gives a compact summary, but it should always be interpreted with the context of the data.
Related ideas include average, median, mode, range, total frequency, frequency table, grouped data, outliers and data interpretation. A clear definition of mean helps students recognise that it is not just any average. It is the average found by sharing the total equally between all values. In exams, always add carefully, divide by the correct number of values and check whether the answer is sensible.