Find Mean, Mode and Median for Grouped data

The Histogram shows an even spread of data, indicating that sometimes the Coffee Shop is very busy, while other times they are making less than eight cappuccinos per hour.We now want to find the Average Number of Cappuccinos made every hour.

There are three types of Averages:

The Mean
The Median
The Mode

In this topic we calculate all three of these averages for the coffee shop example.

Finding the Range

The “Range” is the easiest Statistic to determine for Grouped Data. We simply take the end of the Highest Interval, and subtract the Beginning of the first Interval.

Range = Maximium – Minimum

For our Coffee Statistics, the Highest Group is 16-19, so our High Value “Maximum” is 19. The Lowest Group is 0-3, so the Low Value “Minimum” is zero.

Range = Maximium – Minimum = 19 – 0 = 19
The Range can also be stated as “0 to 19″



The Modal Class

The “Mode” is what happens most of the time, or on most occassions.

The “Mode” is the simplest Grouped Average to find.
It can be read straight from the Frequency Table, or straight from the Graph.

Sometimes we have more than one Group which is the most popular.

In these situations, we can have a two modes or a “Bimodal” situation, or three modes which is called “Trimodal”.

The Median Class

Finding the Median Class involves some working out steps to be applied to our original Frequency Table. There are three Main Steps:

1) Finding the half-way midpoint in the Frequency values.

2) Adding a third column to our Frequency Table where we calculate “Cumulative Frequency” values.

3) Locating the half-way point in the Cumulative Frequency Column, and then seeing which Class Interval lines up with this half-way point.

How we do each of these steps is as follows.

There are two ways to find the half-way midpoint in the Frequency values.

We can either write out the numbers from 1 to the Total frequency value and manually find the middle; or we can use a simple math formula to find this value.

Rather than writing out a long list of numbers, It is much easier to use the formula: 

Middle = Total Frequency + 1 and then divide by 2.