Cumulative frequency graphs, histograms with unequal widths, mean and median

Last time

Before we start: last time, in Back-to-back stem-and-leaf diagrams, box plots and coded totals, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

Grouped data, honest pictures

When data come in classes, you lose the individual values. But you can still read medians and quartiles off a cumulative frequency curve, and draw an honest histogram if you let area, not height, show frequency. Then ask which average suits the data, because one extreme value can wreck the mean.

Cumulative frequency

A cumulative frequency graph plots the running total against the upper class boundary, because that is the point where the total is reached. To find a quartile, go across from the right fraction of the total, then down to the axis. Lower quartile at a quarter, median at a half, upper quartile at three quarters. Always show your lines on the graph. Cambridge awards the method mark for evidence of graph use.

A percentile example

For 120 children, a quarter is the 30th value and three quarters is the 90th. If thirty five percent took longer than T, then sixty five percent took less. That is 0.65 times 120, which is 78. Read across from 78 to the curve, and down. The mark scheme gives T about 28.5 seconds.