# 10.03 Tables and bar charts

Lesson

Data in its raw form is often just a long list of numbers or categories. We can make the data easier to work with by organising it in a table. To visualise the data and more easily make comparisons, or recognise trends, we can display it using a chart.

### Tables for organising data

A table is used to arrange data into rows and columns. Usually the first row or column of the table will have labels that help to identify and organise the data.

Large data sets are often stored electronically in spreadsheets or databases. It is no coincidence that both of these tools are based on tables specifically designed to store, organise and analyse data in a fast and efficient manner.

The following table show the amount of waste produced in a single year by various types of industry in Australia.

Industry type Amount of waste (millions of tonnes)
Households and local councils $13.8$13.8
Construction and demolition $20.4$20.4
Commercial and industrial $20.4$20.4
Coal powered electricity generation $12.3$12.3

The data comes from a report published in November 2018, by the Department of the Environment and Energy. The report stated that during the 2017/18 financial year, Australia generated $67$67 million tonnes of waste, divided amongst four types of industry.

If we display the data using a chart, it becomes even easier to compare the amount of waste generated by each industry type.

The data used in the table above is an example of categorical data, and the column graph is one of several chart types recommended for displaying this type of data. Because the bars are vertical, each category (in this case, the industry type) is displayed along the horizontal axis.

## Bar charts

A bar chart (or bar graph) is used to display categorical data with rectangular bars. The bars can be vertical (like the example above) or horizontal. The height or length of the bars are proportional to the values they represent. Bar charts are a popular choice because they are easy to create and interpret.

### Column graph

When the bars are vertical, like the support columns of a building, the chart is called a column graph (or column chart).

#### Worked example

##### Example 1

The column graph below shows the amount of waste generated each year per person (per capita) in five different countries. In this particular graph, the exact amount (in kilograms) represented by each column is displayed above the column.

Use the graph above to answer the following questions:

1. How much waste was generated during the year by the average Australian?
2. Work out how much waste is generated by an average Australian each day. Assume there are $365$365 days in a year and answer to $1$1 decimal place.
3. How much more waste per person was generated by a citizen of the United States compared with a citizen of the United Kingdom?

Solution

1. The label on the vertical axis indicates that the amount of waste per person is measured in kilograms. From the label above the first column we see that an average Australian citizen generates $1976$1976 kg of waste per year.
2. If we divide $1976$1976 kg by $365$365 days:
 Waste per person per day $=$= $\frac{1976}{365}$1976365​ $=$= $5.413$5.413... $=$= $5.4$5.4 kg (Rounded to 1 decimal place)
3. Here we subtract the amount represented by the UK's column from the amount represented by the US's column.
 Extra waste $=$= $2526-1667$2526−1667 $=$= $859$859 kg

### Horizontal bar chart

If the bars are horizontal, the graph is called a horizontal bar chart, or simply a bar chart. This type of chart can be useful if space restrictions make it difficult to display the bars vertically. It is also a better option for displaying long category labels.

### Side-by-side bar charts

Also known as clustered bar charts or grouped bar charts, these are useful for displaying information about different sub-groups within the main categories. Each sub-group is coloured or shaded differently to distinguish between them, and a legend is used to indicate the subgroup that each colour represents.

The data for a side-by-side bar chart may come from a two-way table, like the one below. The table shows the amount (in kilotonnes) of various categories of waste in Australia that were either recycled or dumped into landfill.

Recycled Landfill TOTALS
Paper and cardboard $3361$3361 $2230$2230 $5591$5591
Plastics $334$334 $2182$2182 $2516$2516
Glass $612$612 $467$467 $1079$1079
Organics $7461$7461 $6710$6710 $14171$14171
TOTALS $11768$11768 $11589$11589 $23357$23357

Notice that the final row and column of the two-way table contain the totals for each row and column. The table above was used to create the side-by-side bar chart below.

Notice that the vertical axis represents the percentage amount allocated to either recycling or landfill, rather than the actual amounts in kilotonnes. For example, the percentage of paper and cardboard that was recycled was calculated as follows:

 Percentage of paper and cardboard recycled $=$= $\frac{3361}{5591}\times100$33615591​×100 $=$= $60.114$60.114... $=$= $60.1%$60.1% (Rounded to 1 decimal place)

### Stacked bar charts

These are similar to side-by-side bar charts, in that they display information about sub-groups. In this case though, the bars are stacked on top of each other to form a single column. These charts are particularly good for displaying the percentage make-up of sub-groups within each category. Once again sub-groups are coloured or shaded differently and a legend is used to identify each sub-group.

Chart design

A chart is a presentation tool. Its whole purpose is to communicate information. For this reason, it must be clear to the person viewing it, what the information represents.

• The title communicates the purpose of the chart. It should include any information relevant to correctly interpreting the data, such as the time period represented, or the location from where the data was collected.
• Each axes should be labelled, including relevant units if appropriate
• The spacing used on the scale for each axis should be consistent across that axis
• For a bar chart, ensure the bars are all the same width. Only the height's of the bars should differ in size, because the height represents the value of the data.
• In a bar chart, it is common to have equal-width gaps between bars. The gaps indicate that the data is categorical. They help distinguish a bar chart from a similar-looking chart called a histogram, which has no gaps between the bars.

#### Practice questions

##### Question 1

Yuri surveyed a group of people about the type of jobs they had. He recorded the data in the following graph.

1. Complete the two way table with the information.

No Job Casual Part time Full time
Men $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
Women $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$

##### Question 2

Members of a gym were asked what kind of training they do. Each responder only did one kind of training. The table shows the results.

Cardio Weight
Male $12$12 $26$26
Female $44$44 $18$18
1. How many gym members were asked altogether?

2. How many members do weight training?

3. What percentage of the gym members do weight training?

##### Question 3

The following stacked bar chart shows different types of internet traffic to a website over a three month period. The vertical axis is the number of visits to the website.

1. What was the total number of visits to the website in November?

Give your answer to the nearest $100$100.

2. During October, how many visitors to the website were new visitors?

3. What proportion of traffic during October were returning visitors?

4. Approximately how many new visitors visited the website during November? Give your answer to the nearest $100$100.

### Outcomes

#### MS11-2

represents information in symbolic, graphical and tabular form

#### MS11-7

develops and carries out simple statistical processes to answer questions posed