Cumulative Frequency

Defining Cumulative Frequency

• Cumulative frequency is a statistical term that refers to the sum of the frequencies of all values up to the current point in a data set.
• Cumulative frequency provides a running total, adding up frequencies cumulatively.
• This method enables us to understand the distribution of data in a range.

Constructing a Cumulative Frequency Table

• Begin by creating a frequency table for the data set.
• For cumulative frequency, add each frequency to the sum of those before it.
• The final value of the cumulative frequency should match the total frequency in your initial frequency table.

Drawing Cumulative Frequency Graphs

• Cumulative frequency graphs, also known as ‘ogives’, provide a visual representation.
• The x-axis should represent the upper boundary of each class interval (from your frequency table), while the y-axis represents the cumulative frequency.
• Plot each cumulative frequency against the upper limit of the corresponding class interval.
• Join the points with a smooth curve. The curve usually starts from the origin and ends at the total frequency.

Interpreting Cumulative Frequency Graphs

• From this graph you can evaluate the median, also known as the second quartile (Q2), that divides the data into two equal halves.
• The first quartile (Q1) and the third quartile (Q3), can be read from the graph which divide the data into four equal parts.
• The interquartile range, calculated as Q3 – Q1, gives a measure of how spread out the middle half of the data values are.
• The range, the difference between the maximum and minimum data value, gives a measure of the total spread of the data.

Remember, the process of acquiring the cumulative frequency from a frequency table assists in understanding how the total frequency changes over an interval. This is a valuable tool for analysing and interpreting data in statistics, allowing you to gain insights about the distribution or spread of data.