Visual Reference / Data handling and probability / Histograms and cumulative frequency

Data handling and probability

Histograms and cumulative frequency

See why unequal class widths need frequency density, then build a cumulative frequency curve and estimate the median.

Curriculum rangeYears 9-11

These classes have different widths, so bar height shows frequency density, not frequency.

0-108

10-2014

20-4020

40-7015

70-1006

\text{frequency density} = \dfrac{\text{frequency}}{\text{class width}}

Class 20-40: 20 ÷ 20 = 1

Learning notes

Histograms and cumulative frequency essentials

Keep these rules beside you while you explore and practise.

1Why histograms are different from bar charts

A histogram is used for continuous, grouped data where classes can have different widths. Bar height shows frequency density, not frequency, so area represents frequency instead.

\text{frequency density} = \dfrac{\text{frequency}}{\text{class width}}

2Finding frequency from a histogram

$\text{Frequency}=\text{frequency density}\times\text{class width}$ -- the same as finding the area of the bar.

3Cumulative frequency

Add up the frequencies as you go, and plot each running total against the upper boundary of its class. Join the points to make a cumulative frequency curve.

4Estimating the median and quartiles

Find half the total frequency on the vertical axis, draw across to the curve, then straight down to read the estimate. Use a quarter and three-quarters of the total for the quartiles.

💡These are estimates, not exact values -- a cumulative frequency curve is drawn from grouped data, so the original individual values aren't known.