Grouped Frequency Tables

Understanding Grouped Frequency Tables

• Grouped Frequency Tables are a means of organising data in statistics.
• They represent the frequency of certain values or ranges occurring in a data set.
• Each grouping or class interval typically covers a range of values and the frequency relates to how many data points fall within that interval.
• The length of each interval is also known as the class width. All class widths should typically be equal in a grouped frequency table.

Creating a Grouped Frequency Table

• List all possible values or ranges in the first column of the table, these are your class intervals.
• In the next column, record the frequency of each value or range, i.e., the number of times it occurs in the data set.
• Choose class intervals that make sense for your data. For example, grouping by tens, hundreds, or simple ranges.
• Your intervals should not overlap. A value should only fit into one class interval.

Interpreting and Using a Grouped Frequency Table

• The total of the frequency column gives you the total number of data points.
• The range, a key measure of spread, can be estimated using the highest and lowest class interval.
• The mode is the class interval with the highest frequency.
• The mid-point of each class interval can be used as a representative value for computations or graphing.

Mean of Grouped Data

• To find the mean using a grouped frequency table, you multiply the frequency of each group by the midpoint of the group.
• Sum these values and divide by the total number of items (total frequency).

Frequency Density

• Frequency density is used when class widths are unequal. It allows data to be plotted accurately on a histogram.
• It is calculated by dividing the frequency by the class width.

Remember, accurate construction and interpretation of grouped frequency tables is crucial in data analysis. Regular practice can enhance your skill in this area of Probability and Statistics.