## What you need to know

A bar graph (or bar chart) is a way of displaying data, typically data split into categories, using bars of different heights. Bar graphs are not the same thing as histograms, and you should make sure to leave gaps between the bars when drawing your bar graph so it doesn’t look like a histogram.

Example: 100 students were asked what their primary mode of transport for getting to school was. The results of this survey are recorded in the table below. Construct a bar graph representing this information.

So, before drawing the bar graph, we have to consider what the requirements of our graph will be from the info in the table:

·         There are 5 categories so it must be wide enough for 5 bars,

·         The highest frequency is 35, meaning the scale on the y-axis must go at least at as high as 35.

Now, remembering to leave gaps between the bars and clearly labelling which bar represents which mode of transport, the resulting bar graph should look like the one shown below.

As you can see, this bar graph displays the information in a clear and obvious way. The bars are very distinct and clearly labelled, and the scale on the y-axis is very readable: 1 small square represents 1 person. Sometimes the scale doesn’t match up quite as well as this, but you should try to avoid scenarios in which each small square is worth some awkward decimal. It makes the chart much harder to read.

In this next example, we’ll look at some questions you might be asked about a bar graph.

Example: A survey was conducted asking people about their favourite flavour of ice cream. The results of this survey are displayed on the bar chart below.

a) Use the bar graph to fill in the gaps in the table.

b) Calculate the percentage of people surveyed whose favourite flavour is strawberry.

a) To fill in the missing gaps in the table, we must read off the height of their corresponding bars from the bar chart. From looking, we can see that each little square is worth 0.5, and so the height of the ‘chocolate’ bar is 12 and the height of the ‘mint choc chip’ bar is 3. Therefore, the completed table looks like the table to the right.

b) From the table, we can clearly see that 5 people chose strawberry as their favourite. To find out what this is as a percentage, we need to work out how many people there were in total.

$\text{Total }=12+16+5+3+6=42$

Therefore, the percentage of people who chose strawberry is

$\dfrac{5}{42}\times 100=11.9\%\text{ (1dp)}$

## Bar Graphs Example Questions

Your bar graph should look like the one shown below. Remember, you must have gaps between the bars and everything (including the axes and the individual bars) should be clearly labelled.

a) So, according to the scale on the y-axis, 5 small squares accounts for 2,000 book sales, so we get

$\text{One small square }=2,000\div 5=400$

So, that means the number of audiobooks sold is 3,200, the number of hardbacks sold is 4,800, and the number of paperbacks sold is 12,000. Therefore, the percentage of sales that were audiobooks is

$\dfrac{3,200}{3,200+4,800+12,000}\times 100=16\%$

b) We’ve already determined the number of hardbacks and paperbacks sold, so the initial ratio is

$4,800 : 12,000$

Cancelling out factors, we get

\begin{aligned}4,800 : 12,000 &= 48 : 120 \\ &=12 : 30 \\ &= 2 5\end{aligned}

This cannot be simplified further, so the ratio in its simplest form is $2:5$.