Cumulative Frequency Graphs

Cumulative Frequency Graphs

1. A way for ESTIMATING the medians and quartiles for large sets of (normally continuous) data.

2. How to draw a cumulative frequency graph

   • You normally start with a table like this: (click on the piece of paper icon at the top right!)
     • Time waiting (min) | No. of passengers | 0 < T ≤ 5                        14 5 < T ≤ 10                      35 10 < T ≤ 15                    26 15 < T ≤ 20                     18 20 < T ≤ 25                       7
     • This needs to be changed into a cumulative frequency table. (like this)
       • Time waiting       Passengers T ≤ 5                       14 T ≤ 10                     (14+35 =) 49 T ≤ 15                    (49+26=) 75 T ≤ 20                    (75+18=) 93 T ≤ 25                     (93+7=) 100
       • Now, plot the graph, with the cumulative frequency (number of passengers) on the y axis, and the time waiting on the x axis. Use a sensible scale, and don't forget to label the axes!
         • Join the points up with a smooth line that goes through every point.
           • To find the median using your graph...
             • Find the middle of the cumulative frequency. (By dividing the total cumulative frequency by 2) In this example, the total is 100, so you are looking for 50
               • Draw a line with a ruler horizontally from the 50 on the cumulative frequency along to where it meets the curved line you drew on the graph to join up the points.
                 • From the point where these two lines meet, draw another line directly downwards, and whatever number this line goes to on the x axis is the median time waiting.
                   • To find the quartiles, do the same as for the median, but with whatever one quarter of the total cumulative frequency is (for the lower quartile) and three quarters of it for the upper quartile.
                     • To find the IQR, find both quartiles using the method above, and then subtract the LQ from the UQ.
         • When plotting, make sure you put the points in the right place along the x axis. eg for the first one, put it on the line where 5 is, nowhere before it.