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# Histograms and frequency density - Higher 0%

Summary

# Histograms and frequency density

## ​​In a nutshell

Histograms are like bar charts but with varying bar widths. Rather than height, it is the area of each bar that shows frequency.

## Drawing a histogram

### ​​Definition

 Class width The difference between the start and end value of the class.

In order to draw a histogram from a frequency table, another quantity needs to be worked out: frequency density - the height of each bar shows this frequency density.

$\text{frequency density} = \text{frequency} \div \text{class width }$​​

#### procedure

 ​​1. Add a frequency density column to table. 2. Draw and label your axes: the y-axis should have the frequency density. the x-axis should have the thing being measured. 3. Draw your bars - remember the width of the bars should correspond to the class widths.

##### Example 1

Below is a frequency table showing the ages of students in a school production. Draw the histogram.

 Age ($a$) Frequency $6​​ ​$4$​​ $10​​ ​$5$​​ ​$12​​ ​$2$​​ ​$13​​ ​$1$​​

 Frequency density ($\text{frequency density} = \text{frequency} \div \text{class width }$) ​$4\div4=1$​​ $5\div2=2.5$​​ $2\div1=2$​​ ​$1\div5=0.2$​​

Now following the steps and drawing the histogram gives:

FAQs

• Question: How do I draw a histogram?

Answer: To draw a histogram: 1. Add a frequency density column. 2. Draw and label your axes: - The y-axis should have the frequency density. - The x-axis should have the thing being measured. 3. Draw your bars - remember the width of the bars should correspond to the class widths.

• Question: What is the equation for frequency density?

Answer: Frequency density = frequency ÷ class width. The height of each bar shows frequency density.

• Question: What is the class width?

Answer: The class width is the difference between the start and end value of the class.

• Question: What is the difference between a bar chart and a histogram?

Answer: Histograms are like bar charts but with varying bar widths. Rather than height, it is the area of each bar that shows frequency.

Theory

Exercises