Cumulative Frequency Curves
Grade 6What cumulative frequency means
Cumulative frequency is a running total of frequencies. Each value in the cumulative frequency column tells you how many data values are less than or equal to the upper boundary of that class.
You plot the cumulative frequency against the upper class boundary — not the midpoint. That's the most common error.
Building the table and plotting the curve
EXAMPLE
Exam marks: 0 ≤ x < 20 (freq 5), 20 ≤ x < 40 (freq 12), 40 ≤ x < 60 (freq 18), 60 ≤ x < 80 (freq 10), 80 ≤ x < 100 (freq 5). Build a cumulative frequency table.
Up to 20: 5
Up to 40: 5 + 12 = 17
Up to 60: 17 + 18 = 35
Up to 80: 35 + 10 = 45
Up to 100: 45 + 5 = 50 (total)
Plot points at (20, 5), (40, 17), (60, 35), (80, 45), (100, 50). Join with a smooth S-shaped curve. The curve starts at (0, 0).
Reading off the median
The median is the value at the halfway point of the data. For 50 values, go across from cf = 25 on the y-axis to the curve, then down to the x-axis.
For n values, the median is at n ÷ 2 on the cumulative frequency axis. Lower quartile is at n ÷ 4. Upper quartile is at 3n ÷ 4.
Watch out for the curve shape
The curve must be smooth and increasing — it can never go down. If your plotted points don't form a rising S-shape, check your running total: you may have added incorrectly or plotted against the midpoint instead of the upper boundary.
