Help your students prepare for their Maths GCSE with this free cumulative frequency worksheet of 21 questions and answers
Suitable for GCSE maths revision for AQA, OCR and Edexcel exam boards
Cumulative frequency is a running total of frequencies. If a set of grouped data is presented in a frequency table, it is useful to add a cumulative frequency column on the right hand side of the table, and record the running totals in here, creating a cumulative frequency table.
On a cumulative frequency graph or cumulative frequency diagram, the data groups are marked on the x axis and cumulative frequency on the y axis. We then plot the endpoint of each group or class interval against its cumulative frequency.
A cumulative frequency curve can be used to estimate the median and quartiles. To estimate the median (the location where 50% of the data lies above and below this value), find the midpoint of the cumulative frequency axis, then read off the corresponding x value. To find the lower quartile, we read off the x value corresponding to one-quarter (25%) of the cumulative frequency axis, and to find the upper quartile, we read off the x value corresponding to three-quarters (75%) of the cumulative frequency axis.
We can use these values, along with the minimum value and maximum value from the graph, to draw an estimated box and whisker plot to represent the distribution. We can also estimate the interquartile range (IQR) by subtracting the lower quartile from the upper quartile.
We can use cumulative frequency curves to compare distributions of two or more data sets by plotting the curves on the same set of axes and comparing the shapes of the curves. This can also be done using their associated box plot.
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