Introduction to grouped frequency tables

Grouped frequency tables categorise data into intervals, or classes, to simplify large data sets.

Each category, known as a class, has a specified range instead of an exact data point.

No overlapping between classes

To ensure each data value fits into a unique class, we use inequalities. 

The first class in the table above contains values which are larger than 5 up to and including 10.

For example, a value of 10.0 falls in the first class, whereas 10.1 would fit into the second.

Determining mid-interval value 

To find this, sum the boundaries of a class and halve the result.

For example, for heights of 5 to 10 mm, the mid-interval value is 25+10​ = 7.5.

The median class contains the  2n + 1​ value. 

Where:

• n = total frequency

For the example above:

Total frequency = 4 + 8 + 6+ 3 + 2 = 23

Location of the median class = 223 + 1​ = 12

The 12th value lies within the 110 < h ≤ 120 class, making this the median class.

The range can be identified by subtracting the minimum value from the lowest class from the maximum value from the highest class.

In the example above the range = 150 - 100 = 50 cm

Estimating mean from group data

To calculate the mean from a grouped frequency table:

1. Insert a third column for mid-interval value.
2. Add a fourth column titled frequency x mid-interval value.
3. Calculate the total frequency and total (frequency x mid-interval value).
4. Mean = total frequencytotal (frequency x mid−interval value)​

Example:

Worked Example 1: Identifying the mean from a grouped frequency table 

Calculate the mean from the grouped frequency table below.

1. Insert a third column for mid-interval value. 
2. Add a fourth column for frequency x mid-interval value.
3. Calculate the total (frequency x mid-interval value).
4. Mean = total frequencytotal (frequency x mid interval value)​