Skip to main content
MathidiaMathematics Academy
Statistics and distributions
Lesson 61 of 75
Introduction

Histograms

Objective. Use frequency density with unequal class widths.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Histograms display continuous grouped data using frequency density on the vertical axis, which allows for bars of unequal class width unlike a bar chart. Frequency density is calculated as frequency divided by class width, and the area of each bar, not its height, represents the frequency for that class. For example, a class of width 5 with frequency 20 has frequency density 4, so the bar is drawn with height 4 over a width of 5. To find a missing frequency from a histogram, multiply the bar's frequency density by its class width.

Worked example

A histogram bar for the class 10–25 has frequency density 3. Find the frequency represented by this bar in the histogram.

10253
Bar chart of the values 10, 25, 3
  1. 1Class width = 25 − 10 = 15
  2. 2Frequency = frequency density × class width
  3. 3Frequency = 3 × 15
  4. 4Frequency = 45

Answer: 45

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. Students often read the bar's height straight off as the frequency; remember frequency equals area (height × width), so unequal class widths must be accounted for before comparing bars.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard