Cumulative Frequency Graphs (DP IB Applications & Interpretation (AI)): Revision Note

Cumulative Frequency Graphs

What is cumulative frequency?

• The cumulative frequency of x is the running total of the frequencies for the values that are less than or equal to x

• For grouped data you use the upper boundary of a class interval to find the cumulative frequency of that class

What is a cumulative frequency graph?

• A cumulative frequency graph is used with data that has been organised into a grouped frequency table

• Some coordinates are plotted

  • The x-coordinates are the upper boundaries of the class intervals

  • The y-coordinates are the cumulative frequencies of that class interval

• The coordinates are then joined together by hand using a smooth increasing curve

What are cumulative frequency graphs useful for?

• They can be used to estimate statistical measures

  • Draw a horizontal line from the y-axis to the curve

    • For the median: draw the line at 50% of the total frequency

    • For the lower quartile: draw the line at 25% of the total frequency

    • For the upper quartile: draw the line at 75% of the total frequency

    • For the p^th percentile: draw the line at p% of the total frequency

  • Draw a vertical line down from the curve to the x-axis

  • This x-value is the relevant statistical measure

• They can used to estimate the number of values that are bigger/small than a given value

  • Draw a vertical line from the given value on the x-axis to the curve

  • Draw a horizontal line from the curve to the y-axis

  • This value is an estimate for how many values are less than or equal to the given value

    • To estimate the number that is greater than the value subtract this number from the total frequency

  • They can be used to estimate the interquartile range 

  • They can be used to construct a box plot for grouped data