How to draw and use….. Cumulative frequency graphs

Cumulative frequency is just… A running total

Look at these tables Age, a (years) Frequency 5 < a ≤ < a ≤ < a ≤ < a ≤ < a ≤ 60 5 Age, a (years) Cumulative frequency ≤ 123 ≤ 2012 (3+9) ≤ 3029 (3+9+17) ≤ 4039 ( ) ≤ 6044 ( )

Once we have calculated the cumulative frequency We don’t need the frequency any more.

We can use our results to draw a cumulative frequency curve Age, a (years) Cumulative frequency ≤ 127 ≤ 2019 ≤ 3036 ≤ 4042 ≤ 6044 Along the ‘x’ axis Up the ‘y’ axis

Plot the points Cumulative frequency Age (years)

Draw the curve Cumulative frequency Age (years)

Now draw in the median Remember it is halfway up the cumulative frequency axis – in this case 22

Median…… Cumulative frequency Age (years) halfway up Read off here

The median is …….. (about) 26.

Now for the lower quartile Quarter of the way up the Cumulative frequency axis

Lower Quartile Cumulative frequency Age (years) – quarter of 44 Read off here

So the lower quartile is …. 19

Upper quartile Three quarters of the way up the Cumulative frequency axis

Upper quartile Cumulative frequency Age (years) – three quarters of 44 Read off here

The upper quartile is …. 32

Inter-Quartile range Upper quartile – lower quartile

Inter-quartile range = 13

Try this one ….. Salary (£) Frequency Salary (£) Cum. Freq

Cumulative frequency Constructing a cumulative frequency table Using a cumulative frequency graph to construct a box and whisker diagram

A golf club has 200 members. Their ages are shown in the frequency table below. Age (a years)Frequency 0 ≤ a < ≤ a < ≤ a < ≤ a < ≤ a < ≤ a < ≤ a < ≤ a < Age (a years)Cumulative frequency a < 10 a < 20 a < 30 a < 40 a < 50 a < 60 a < 70 a < A cumulative frequency (or a “less than”) table can be drawn from this data. How old is the youngest/oldest person?

Age (a years) Cumulative frequency a < 10 a < 20 a < 30 a < 40 a < 50 a < 60 a < 70 a < We can now use this to draw a cumulative frequency graph.

Age (a years) Cumulative frequency a < 10 a < 20 a < 30 a < 40 a < 50 a < 60 a < 70 a < We can now use this to draw a cumulative frequency graph.

Cumulative Frequency graph. We can now use this to find the following information.. Median Lower quartile Upper quartile Lowest Value Highest Value This information can now be used to draw a box and whisker diagram.. 80 Interquartile range