Math Figures Cumulative Frequency Graph Generator
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Cumulative frequency graphs from a frequency table

The Cumulative Frequency Graph Generator draws a cumulative frequency graph from a frequency table, a cumulative table or a data set. Each point is plotted at a bin’s upper bound against the running total up to it, starting from 0 at the lowest bound, and the points are joined by a smooth curve or straight lines. The axes fit the data unless you type their ranges.

Dashed lines read the median and quartiles off the curve, or any percentile, or go up from a value to estimate how many are below it. Each value is written at the axis, left as a blank line for students, or left off. Every reading is taken from the curve as drawn, so it matches what students measure on the printed graph.

What you can set

  • The data: a frequency table of each bin’s upper end and frequency, a cumulative table of upper bounds, or a data set sorted into bins of a width you choose, with no inequalities to type
  • Crosses or dots at the points, joined by a smooth curve, straight lines or nothing, starting from 0 at the lowest bound or not
  • A vertical axis of cumulative frequency or cumulative percent
  • Reading lines for the median, lower and upper quartiles, any percentile, across from a cumulative frequency or up from a value, each with its value, a blank line or neither
  • Color, or black and white for printing
  • A chart title and axis titles, as text or a blank line for students
  • Each axis’s range and count-by, worked out from the data unless you type them, which lines are numbered, and the gridlines

Copying, printing and sharing

Copy the figure straight into a test, worksheet or slide, or download it as a PNG or SVG. Printing the page prints just the figure. Share link copies the page’s address with your settings in it, so anyone who opens it sees this exact figure, and presets save settings you use often in your browser. It’s free, with no sign-up.

Example figures

Frequently asked questions

Where are the points of a cumulative frequency graph plotted?

At the upper bound of each bin, against the running total up to that bound. The graph starts with a point at the lowest bound and 0, as GCSE mark schemes expect; turn off Start from 0 at the lowest bound to leave it out.

Is a cumulative frequency graph the same as an ogive?

Yes. US textbooks often call it an ogive and draw it with straight lines and a percent axis. Choose Straight lines under Join and Cumulative percent for the vertical axis to draw it that way.

How are the median and quartiles found?

A dashed line runs across from half of n (a quarter and three quarters for the quartiles) to the curve, then down to the horizontal axis. The value is read where that line meets the curve as drawn, to a tenth of a block, so a smooth curve and straight lines can give slightly different answers, as they do on paper. The panel lists the median, quartiles and interquartile range.

Can I type a cumulative frequency table instead?

Yes. Choose Cumulative table, type where the first bin starts, then each upper bound with its running total, or paste the table. The curve starts from 0 where the first bin starts.

How do I make a graph for students to draw on?

Choose None under Join for the points alone, so students draw the curve. For blank axes, leave the data empty and type each axis’s range. To have students read a value, draw its lines and choose Blank for its value.

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