Grouped Frequency Tables

• Grouped frequency tables are used to organise and display data that comes in ranges rather than individual values.
• It helps understand the distribution of data over different intervals, thereby providing insights into the overall data spread.
• The first column lists the intervals or groups of values. These intervals should be equal in size.
• The second column records the frequency of data. It shows how many times the values in the corresponding interval occur in the data set.
• To find these frequencies, tally marks can be used first, and then converted into numbers.
• Cumulative frequency can also be displayed in another column. Cumulative frequency is the running total of the frequencies. For each group, it is the frequency of that group added to the frequencies of all previous groups.
• A midpoint column can also be added. The midpoint of a group is the average of the lower and upper boundaries of the group.
• The data collected is often called raw data, and placing it into a grouped frequency table forms organised data.
• This type of table is particularly helpful when dealing with a large set of data.
• When the data ranges are not stated, they can often be found out by finding the difference between the lowest and highest value in the data set and dividing this by the number of groups.
• Sometimes the table might include a row for ‘frequency density’ which is calculated as frequency divided by class width. This allows for comparison between groups of different widths.
• Grouped frequency tables often serve as a useful stepping stone for further statistical calculations or representations such as histograms and cumulative frequency graphs.