Cumulative frequency graphs

The common mistake

Plotting cumulative frequency at the midpoint of each class instead of at its upper boundary, which shifts the whole curve and every estimate read from it.

Instead: Add a running-total column. Plot each total at the top of its class, because that's when all those values have been counted. Start the curve at the lower boundary of the first class with 0. For the median, read across at half the total; for quartiles, at a quarter and three quarters.

Worked example with Guide me

Times: 0–10 min: 4 people, 10–20: 10, 20–30: 6. Where do you plot the points, and what's the median position?

1. Sugar · What are the running totals?
   Student · 4, 14, 20.
2. Sugar · Where does the point for 14 go?
   Student · At 20 minutes, the upper boundary of 10–20.
3. Sugar · Total is 20. Where do we read the median?
   Student · Across at 10 on the cumulative axis.

Answer: Plot (0, 0), (10, 4), (20, 14), (30, 20); read the median at cumulative frequency 10.

Quick answers

What is the most common mistake with cumulative frequency graphs?

Plotting cumulative frequency at the midpoint of each class instead of at its upper boundary, which shifts the whole curve and every estimate read from it.

How do I get cumulative frequency graphs right?

Add a running-total column. Plot each total at the top of its class, because that's when all those values have been counted. Start the curve at the lower boundary of the first class with 0. For the median, read across at half the total; for quartiles, at a quarter and three quarters.

Can you show a worked example?

Times: 0–10 min: 4 people, 10–20: 10, 20–30: 6. Where do you plot the points, and what's the median position? Plot (0, 0), (10, 4), (20, 14), (30, 20); read the median at cumulative frequency 10.

Related concepts

• Multiplying probabilities for “and” events
• Checking whether events are independent