Reading Cumulative-Frequency Graphs
A cumulative-frequency graph works in both directions: start with a value to find a count, or start with a count to estimate a value.
62% of 250 = 155.0 → estimated value 22.8
A hand-drawn smooth curve may give a nearby value. Use the curve you actually drew.
Translate the words into a cumulative count
| Question wording | Operation |
|---|---|
| fewer than v | read cf(v) |
| more than v | total − cf(v) |
| between a and b | cf(b) − cf(a) |
| smallest k values | read a value at cf = k |
| largest k values | read a value at cf = total − k |
A proportion is handled the same way. If 38% are at or above a value, then 62% are below it. For 250 observations, read the graph at .
Convert a percentile before touching the graph
The p-th percentile is a value with about of the observations below it. For a total of , first calculate . Move across from that cumulative frequency to your curve, then down to the value axis.
- A plotted cumulative-frequency point is exact for the grouped table.
- A read between plotted points is an estimate from the curve you drew. Do not replace it silently with straight-line interpolation.
- To compare two curves, read both values at the same cumulative proportion. A curve further to the right gives the larger value at that proportion. If curves cross, the comparison can change.
Percentage → cumulative count → across to the actual curve → down to the value. Show the guide or calculation so the graph use is visible.
Now you try
The cumulative-frequency curve is for 250 leaf lengths. 38% of the leaves have length cm or more. Use the graph to estimate .
Show worked answer
The proportion below is . Calculate . Read across from cumulative frequency 155 to the smooth curve and down to the length axis. A correct graph gives about . Nearby readings are possible because this is a graph estimate.