A **bar chart** is probably the most popular way of presenting data. Later we will also look at a **histogram**, which is more complicated form of bar chart for **continuous data**.

The basic principle of a bar chart is that:

- one axis contains
**categories**, e.g. eye colour: brown, blue, green, grey; - the other axis displays
**frequency**, e.g. how many people have that colour eyes.

Normally the frequency axis is the y-axis, but not always.

As usual, the axis must go up in equal steps, preferably with 5-10 steps marked on its scale.

**Example** **with Teacher**:

The following shows the scores of 36 students in a spelling test. Put the information first into a tally chart and then into a bar chart:

**Exercise for Students:**

Two dice were thrown sixty times, and the below table shows the score recorded each time:

Put this information into a tally chart and then present the data on a bar chart.

**Grouping Data**

Often it is not practical to show a different bar for every value, and so we group the data. For instance, if wanted to compare how many people of each age were in a rock concert, instead of having 60 different bars, it would be more useful to group the people into age groups, e.g. 1-10, 11-20, 21-30, etc.

A **sensible** number of groups is typically 5-10 groups.

**Example** **with Teacher**:

Let’s decide on sensible groups for the below data, and put it into a tally chart and then draw the corresponding bar chart:

Second worked example:

Below are the answers:

**Histograms – Extension Work**

A histogram is similar to a bar chart, but is primarily for continuous data (e.g. weight, height). It is especially effective where we have grouped data where the groups have different sizes.

With a histogram, instead of the **height of the bar** representing frequency, it is the **area of the bar** that represents frequency.

In order to make this happen, the y-axis should show not **frequency**, but instead** frequency density**. We calculate frequency density as **frequency ÷ class width**.

Read through the below example on drawing a histogram, then complete exercise 4 on page 341 of the extended text book. The questions from this book are detailed below.

**Example**

**Question Set:**

**Answers**