Mean (Grouped Data)

Introduction: When the List Is Too Long to Add One by One

You already know how to find an average. Add up all the numbers, then divide by how many numbers there are. If three friends scored 8, 6 and 10 in a test, their average is $\dfrac{8 + 6 + 10}{3} = 8$.

That works when you have a short list. But what happens when you have the marks of 300 students? Or the daily rainfall of a village for a whole year? You are not going to add 300 numbers one at a time on a phone. You will lose count. You will make a slip.

So people do something clever. They bunch the data into groups — "10 to 25", "25 to 40", and so on — and just count how many fall in each group. This is called grouped data: data sorted into class intervals with a frequency (a count) for each one.

Here is the problem that creates. Once you bunch the marks into "40 to 55", you no longer know each student's exact mark. You threw that away. So how can you find an average when you do not have the original numbers anymore?

That is the whole story of this topic. By the end, you will be able to find the mean of grouped data three different ways — and you will know which way to pick.