Cumulative frequency, box plots and histograms

Cumulative frequency

Cumulative frequency is a running total.

Plot each running total at the top of its class (the upper class boundary), start at zero at the bottom of the first class, and join the points with a smooth curve.

With 60 values, read across from 30 for the median, from 15 for the lower quartile and from 45 for the upper quartile. Here the median is about 25 minutes and the quartiles are about 18 and 32. The interquartile range = upper quartile − lower quartile: the spread of the middle half of the data, which an extreme value does not affect. Here it is about 32 − 18 = 14 minutes.

To count how many are more than a value, read up from the value to the curve and across: that is how many are at or below it. Take it from the total: if 12 of 60 took 15 minutes or less, then 60 − 12 = 48 took more than 15 minutes. From a cumulative frequency table, "more than 40" is the total minus the running total at 40.

For a list of n values in order, the lower quartile is the (n + 1) ÷ 4 th value and the upper quartile is the 3(n + 1) ÷ 4 th value. For 11 values: the 3rd and the 9th.