Grouped Frequency Tables

Grouped Frequency Tables

  • A grouped frequency table is a way to display data in groups (also known as bins or classes) rather than individually.
  • These tables are particularly useful in dealing with large data sets.

Creating a Grouped Frequency Table

  • The first step is to determine the range of the data, by subtracting the lowest data value from the highest.
  • Next, decide on the number of intervals or groups. Suitable group numbers could be 5, 10, 20 etc. The number of groups generally depends on the size of the data set and the level of detail required.
  • The width of the interval is then calculated by dividing the range by the number of groups. If the interval width is not a whole number, it is usually rounded up.
  • A tally mark is used to mark each data point that falls within an interval.
  • The frequency of each group is then calculated by counting the tally marks.

Features of Grouped Frequency Tables

  • Each group or class contains a lower class boundary (the smallest number in the class), a higher class boundary (the largest number in the class), and a class width (the difference between the lower and higher class boundaries).
  • The mid-point (also known as the class mark) of each class is calculated as the average of the lower and higher class boundaries.

Advantages of Grouped Frequency Tables

  • Grouped frequency tables can simplify complex data and make it easier to identify trends and patterns.
  • It provides a summary of the data distribution.

Disadvantages of Grouped Frequency Tables

  • An important limitation of a grouped frequency table is that some detail is lost by grouping the data. The exact values and their frequency no longer appear in the table.
  • Tables could be misleading if the groupings or data intervals are not chosen carefully.

Interpreting Grouped Frequency Tables

  • The mode can be estimated as the mid-point of the group with the highest frequency.
  • The mean and median can be estimated using grouped data, but the process is more complicated.
  • An Ogive (cumulative frequency graph) can be drawn from a grouped frequency table to help visualise the data distribution.