Cumulative frequency and histograms · Year 11

In Year 11 you learn: histograms.

When data are grouped into classes, cumulative frequency (a running total) lets you estimate the median and quartiles from a graph. Histograms show grouped continuous data. The AREA of each bar is the frequency, so the classes can have different widths.

Key facts

  • Cumulative frequency is the running total of the frequencies.
  • Plot each cumulative frequency at the upper end of its class and join the points.
  • Median ≈ the value at n/2 on the cumulative frequency axis. Q1 is at n/4 and Q3 at (3n)/4.
  • Frequency density = frequency ÷ class width. So frequency = frequency density × class width.
  • Estimated mean of grouped data = Σ(f × midpoint) ÷ Σf.
  • The modal class has the highest frequency density, which is not always the highest frequency.

Worked examples

Example 1

In a histogram, the bar for 20 < a ≤ 40 has a frequency density of 1.5. How many values are in that class? Estimate how many are between 25 and 40.

Answer: 30; about 22.5

Other years