Unit 3 – Statistics (Higher) · Higher
Histograms & Cumulative Frequency
Drawing and interpreting histograms (frequency density), cumulative frequency curves, medians and interquartile range.
Histograms are used for continuous grouped data when class widths vary. Cumulative frequency helps find medians and quartiles from grouped data.
Histograms
Frequency density = frequency / class width
The **area** of each bar represents the frequency (not the height alone).
Unequal class widths are common – always use frequency density on the vertical axis.
Worked example
Class 10–20 has frequency 40. Frequency density?
Solution
Width = 10, FD = 40 / 10 = **4**
Cumulative frequency
Running total of frequencies.
Plot upper class boundary against cumulative frequency.
• **Median** – read off at n/2
• **Lower quartile** – at n/4
• **Upper quartile** – at 3n/4
• **IQR** = UQ − LQ
Box plots show min, LQ, median, UQ, max at a glance.
Practice questions
Try these without looking at the answers first.
Q1.Frequency 30, class width 5. Frequency density?
Show answer
6
Q2.For 80 values, at what cumulative frequency do you read the median?
Show answer
40
Q3.IQR = ?
Show answer
Upper quartile − lower quartile