Drawing Histograms

 

What Is a Histogram?

A histogram is a type of bar chart used for continuous grouped data. 

It shows how data is spread out across different intervals.

Key Differences from a Bar Chart:

• Bar Chart: Used for discrete or categorical data; gaps between bars.
• Histogram: Used for continuous data; bars are touching, and area (not height) represents frequency.

 

How Do You Draw a Histogram?

Step 1: Calculate Class Widths

$$\text{Class Width} = \text{Upper limit} - \text{Lower limit}$$

Step 2: Work Out Frequency Densities

Use the formula:

$$\text{Frequency Density} = \frac{\text{Frequency}}{\text{Class Width}}$$

Step 3: Draw the Bars

• The x-axis represents the class intervals.
• The y-axis represents the frequency density.
• Bars must be touching, and their area should represent the frequency.

 

Example

A coach records how long (in minutes) it takes 30 runners to finish a training circuit.

 

Time (mins)	Frequency
10-20	6
20-25	10
25-30	8
30-40	4
40-60	2

 

Step 1: Find Class Widths and Frequency Densities

 

Time (mins)	Freq.	Width	Freq. Density
10-20	6	10	0.6
20-25	10	5	2.0
25-30	8	5	1.6
30-40	4	10	0.4
40-60	2	20	0.1

 

Step 2: Draw the Histogram

• On the x-axis, label the time intervals: 10–20, 20–25, 25–30, 30–40, 40–60.
• On the y-axis, label frequency densities: 0 to 2.5 (depending on max value).
• Each bar should:
  • Start and end at the correct class boundaries.
  • Have height equal to the frequency density.