Cumulative frequency
Cumulative frequency is a running total of the frequencies. Plotting cumulative frequency against the upper class boundary and joining the points gives a smooth cumulative frequency curve (an ogive).
Key idea
For n data values read from the curve: median at the n⁄2 value, lower quartile Q₁ at n⁄4, upper quartile Q₃ at 3n⁄4. Interquartile range = Q₃ − Q₁.
Histograms with unequal widths
When classes have different widths, the vertical axis shows frequency density, not frequency, so that area represents frequency.
Key idea
frequency density = frequency ÷ class width, so frequency = frequency density × class width.
Worked example
Worked example
A class covers 20 ≤ x < 40, so its width is 20, and it contains 50 values.
Frequency density = 50 ÷ 20 = 2.5.
The bar is therefore drawn 2.5 units high. A wide class with the same frequency would be drawn shorter, keeping the area fair.
Remember
- On a cumulative frequency curve, plot at the upper boundary of each class.
- In a histogram, frequency = area of the bar.
- The interquartile range measures the spread of the middle half of the data.