Frequency Tables

Understanding Frequency Tables

  • Frequency tables are an essential tool in statistics for organising raw data.
  • They provide a quick overview of data, simplifying the process of understanding it.
  • A frequency table shows the number of times that each data value, or group of data values, occurs.
  • The data values are listed down one side of the table - these are usually sorted in ascending or descending order.
  • The frequencies (the number of times each value occurs) are listed down the other side of the table.
  • The two main parts of a frequency table are the data column (which lists each individual data point or group) and the frequency column (which lists how often each data point or group appears in the dataset).

Creating Frequency Tables

  • Choose an appropriate data range (for example, if recording scores on a test, you might choose a range from 0 to 100).
  • Use the data to determine what categories or bins will be used in the table - these must cover the entire data range.
  • Tally the data, adding one to the tally in the appropriate category each time a data point in that category is observed. This is the frequency of that category.
  • Be sure to verify accuracy by adding up the frequency count and compare with the total amount of data.

Interpreting Frequency Tables

  • The total of the frequency column should equal the number of data points in your dataset.
  • A frequency table does not show the original data points, but an overview of the data range.
  • Activity frequencies in different categories can be compared to identify patterns or trends.
  • In some cases, you might be interested in working out the mean from a frequency table by finding the total of (midpoint × frequency) for each group, and then dividing by the total frequency.

Cumulative Frequency Tables

  • Cumulative frequency is the running total of the frequencies.
  • This type of table can be used to find the median and interquartile range.
  • To calculate cumulative frequency, add up the frequencies from top to bottom of the table.
  • Plotting the cumulative frequency can help visualise data and is used to draw a Cumulative Frequency Graph.

Remember, while frequency tables can simplify raw data, they also remove detail. Always bear in mind what has been left out when interpreting a frequency table.