An average or measure of central tendency is a single value that indicates the approximate size or typical value of the numbers in the set. The three most common measures of central tendency, informally known as averages, are given by the mean, median and mode.

The best way to illustrate the differences between the mean, median and mode is to consider a given set of numbers. For example, consider the following:

3, 5, 1, 4, 5,


The mean is found by adding all of the data values together and dividing by how many there are. For the set of numbers given above the mean is given by:


The mean of the set is 3.6.

For grouped data… (is the midpoint calculation the same as the interpolation?)


The median is the middle data entry once all of the data values have been put into ascending order:

1, 3, 4, 5, 5

The middle data point is 4 and so the median of the set is 4.

Note that the middle data entry is only explicitly clear when there is an odd number of data points. When then number of data points is even….

Intro to interpolation…

Quartiles and Percentiles

For discrete data..
For continuous data use interpolation…


The mode is the most common number in the given set of numbers. For the set above, the most common number is 5, hence, the mode is 5.

For grouped data, rather than the mode which is a single number, we are often the most common interval or class. This is known as the modal class.

The above examples illustrate how to find measures of central tendency (or averages) for grouped discrete data. The introduction of additional numbers or the removal of numbers affects the different averages in different ways. For example,… Other examples may include identifying the missing numbers given certain snippets of information.

Also see Measures of Variation.