# 2 Tables and charts

## 2.4 Bar charts and frequency diagrams

Pie charts are useful for showing proportions, but different types of chart have to be used for representing other kinds of
data. A number of these charts are described in this section. The most well known is the **bar chart**.

A bar chart can be seen below. The length of each bar represents the diameter of the planet. Among other things, the chart shows that the diameter of the Earth is about 13 000 km.

The bars on a bar chart are usually drawn not touching one another. Furthermore, to prevent a bar chart giving a misleading representation of the data, the bars should be the same width, and the scale (in this case, the diameter of the planet) should start from zero and be clearly labelled.

In the bar chart above, a numerical value is associated with each planet. In a similar way, a bar chart could be drawn representing, for example, the distances travelled in one hour by different modes of transport: on foot, by bicycle, etc. Again, a numerical value (distance travelled) would be associated with each category (foot, bicycle, etc.). For data of this kind, bar charts are usually the most suitable form of representation.

Another kind of data relates to *how many* items there are in a particular category. Such information is often presented in tables that are known as **frequency tables** – the frequencies are the number of times that each possibility occurred.

In some cases, the information given in a frequency table can be represented by a bar chart, but in other cases the nature
of the data means that another kind of chart (as described later in this section) is required. For convenience, diagrams produced
from frequency tables, whether bar charts or some other kind of chart, are all called **frequency diagrams**. Bar charts can be drawn with either horizontal or vertical bars but frequency diagrams often have veritcal bars.

### Example 7

This frequency table shows the number of children per household in a sample of 30 households. Draw a frequency diagram in the form of a bar chart to illustrate the information.

The bars in a bar chart can be drawn either horizontally or vertically. For example, the bar chart in Example 5 could have been drawn as follows:

It is important to appreciate that frequency diagrams in the form of bar charts are used only when data are collected in separate
categories. Such data, called **discrete data**, are gathered by *counting* things. They include data that can only take certain values and cannot have intermediate values (for example, family size,
which can only take whole numbers, or shoe size, which can only take whole and half numbers).

A different kind of frequency diagram is used to represent **continuous data** – data that are *measured* rather than counted (for instance, people's heights and weights, times taken for journeys or phone-calls). The distinction
between discrete and continuous data shows up visually in frequency diagrams according to whether or not there are gaps between
adjacent bars: thus, a frequency diagram for *discrete* data (that is, a bar chart) should have these gaps (to emphasise that the data are in separate categories), but a frequency
diagram for *continuous* data should be drawn with a continuous scale and with adjacent bars touching (to emphasise the continuous nature of the data).
Note that not all charts published adhere to this rule. You will meet the term ‘histogram’ for some kinds of frequency diagram
used to represent continuous data.

Below is an example of a frequency diagram for continuous data. It represents the birthweights of 23 babies, as given in the table.

Birthweight/grams | Number of babies |

Above 1750 up to and including 2250 | 1 |

Above 2250 up to and including 2750 | 0 |

Above 2750 up to and including 3250 | 5 |

Above 3250 up to and including 3750 | 12 |

Above 3750 up to and including 4250 | 4 |

Above 4250 up to and including 4750 | 1 |

Notice that frequency diagrams for *continuous* data always have the frequencies shown vertically, while the horizontal scale is continuous. Also notice how the bars are
drawn: the lines showing the divisions between each bar are at the boundaries between the groups of data (that is, at 2250
g, 2750 g, 3250 g, etc.). The *height* of each column shows the number of babies whose weights are in each group.

Sometimes you may want to compare the data given in two or more frequency diagrams. The two frequency diagrams for continuous
data that are set out below show the waiting time until the first clinical assessment at the A&E departments of two hospitals,
*A* and *B*. The waiting times of 300 people were surveyed for each hospital.

Click on ‘Hospital A’ or ‘Hospital B’ to see the respective frequency diagrams.

These frequency diagrams show that for Hospital *A*, the most often reported time waiting was between 30 and 35 minutes, while for Hospital *B* it was between 10 and 15 minutes.

### Try some yourself

**1** The frequency diagram below shows the numbers of people in different age groups in a sample of the UK population.

- (a) What is the width of each age group?
- (b) Which age group contains the largest number of people?

- (a) The width of each age group is 10 years. For example, the ten ages 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 years make up the first age group.
- (b) The largest number of people are in the age group 10 and above but less than 20 years.

**2** The bar chart below represents the numbers of cars predicted to be sold by one company in nine successive years.

- (a) How many cars were predicted to be sold in 2010?
- (b) How many cars were predicted to be sold in 2015?
- (c) What does the bar chart suggest about the pattern of predicted sales?

- (a) About 12 000.
- (b) About 21 000.
- (c) Generally the sales figures are increasing, although there was a slight fall in 2012.

**3** This table summarises the results of a survey of 300 people who were asked how long it took them to get from Central London
to Heathrow Airport.

Time/mins | Number of people |

30–35 | 30 |

35–40 | 60 |

40–45 | 110 |

45–50 | 50 |

50–55 | 30 |

55–60 | 10 |

60–65 | 10 |

Total |
300 |

- (a) Illustrate the information by means of a frequency diagram. (You may find it easiest to draw your frequency diagram on graph paper.)
- (b) What does the width of each interval represent?