The average or arithmetic mean (often abbreviated to just the ‘mean’) represents a convenient way to summarise a series of numbers to give a rough indication of a typical value.
The average or mean of a set of numbers is calculated as the sum of those numbers divided by the count of the numbers.
Thus the average age or mean age is 30 years of three people who are aged 28, 30 and 32 years (the sum 90 years is divided by the count 3 to give the average or mean of 30 years).
The average or mean is a summary statistic as it represents a summary of a set of data. There are alternative methods and summary statistics where the data or series of numbers are not symmetrical (or have a skewed distribution). For instance, where there are 10 people are aged 26, 28, 29, 29, 30, 31, 31, 32, 32 and 90 years, the average or mean age is 35.8 years which does not really represent the ‘typical’ age of these individuals as the majority are around 30 years and one person is 90 years. However, here the distribution (or set of values) of the ages are skewed because there is a small number of observations (or values) which are very high in relation to the remaining values. If the distribution is skewed, then the mean does not necessarily give a true picture of a ‘typical’ value, in which case, other summary statistics are more appropriate, such as the mode or median.