An introduction to design engineering

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# Histograms and bar charts

The following section provides further information about histograms and bar charts.

## Box 6 Histograms and bar charts

Histograms:

• are used to show distributions of variables
• plot quantitative data, grouped into intervals, i.e. a number, or a range of numbers.

In a histogram:

• the bars appear in numerical order
• there are no spaces between the bars (unless the number of occurrences in a particular range is zero)
• the area of each bar represents a proportion, or percentage, of the total.

Bar charts:

• are used to compare variables
• plot categorical data, e.g. colour, flavour, gender, occupation.

In a bar chart:

• the bars can appear in any order
• there are spaces between the bars
• the height of each bar represents the quantity of interest.

## Activity 11 Other people’s data

Timing: Allow 20 minutes to complete this activity

To make sense of what this histogram is showing, do the following:

• Look over the whole graph to get a sense of the information.
• Look at the horizontal and vertical axes to understand what units are being displayed (and how they are displayed).
• Roll your cursor over the vertical bars to get detailed data on each ‘bin’.
• Click on the ‘Male’, ‘Female’ and ‘Combined’ (total) labels at the bottom of the figure to switch these values on or off.
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### Discussion

On the horizontal axis, there are a series of ‘bins’. Each bin represents a short range of a continuous measurement – in this case, height – and each bin represents 0.1 metres. For each bin, there is a frequency (vertical axis) which tells you how many data points are in each bin.

The height of each bar represents the number of people who are in a particular height range. This information has been further divided by gender.

Now make use of this histogram in the following activity.

## Activity 12 Finding data ranges

Timing: Allow 20 minutes to complete this activity

Using the histogram in Activity 11, find which data range you are in.

1. How many people in total are in the same data range as you?
2. How many men and women are in the same data range as you?

### Discussion

The answer to this will depend on your height! To find the correct answer you have to first identify which data range you are in. For example, if you are 1.68 m tall you will be in the range 1.6–1.7 m.

Once you have the appropriate data range you can roll your cursor over the vertical bars (coloured blue, black and green) to get the numbers of male, female and combined (total) in that range.

In Activity 12 you identified which range your own height was in, as well as how many other people were in that same range from the sample data.

For this data to be really useful you need a few more data points, and the ranges would be more useful if they were smaller, as in Figure 15. Based on the data in Figure 15, 18% of the population are in the 1720–1739 mm bucket. This means that 18% of people are between 1720 mm and 1739 mm tall. Another way to write this is by using a tolerance symbol (±), so in this case the tolerance is (to a good approximation) 10 mm above or below 1730 mm. This can be written as 1730 (±10) mm.

## Activity 13 Percentages and populations

Timing: Allow 20 minutes to complete this activity

In Activity 8 you worked out your new perfect desk height. Now assume that this desk height is directly related to your own height.

Use the data in Figure 15 to work out:

• a.Which bucket does your height fall into? Write this bucket as a value with a tolerance.
• b.What percentage of the population is in that same bucket (i.e. what percentage might be satisfied with your desk height)?
• c.What percentage of the population of 200 people is outside that bucket (i.e. what percentage might not be satisfied with your desk height)?

### Discussion

The answers to this will depend on your own height. In these example answers a person of 1762 mm height has been used.

• a.1770 (±10) mm bucket (because 1762 mm is within the 1760–1779 mm range).
• b.11% (estimated from the vertical axis (y-axis) on the histogram in Figure 15).
• c.The percentage outside this range can be found by either adding up all the other percentages (a very slow process) or subtracting 11% from 100%, to give 89%.

From this activity it seems that quite a few people might not be entirely happy with your specific desk height. A next step might be to work out a bit more accurately what sort of height ranges would be acceptable to suit as many people as possible.

But there are a few big assumptions in what you have just done.

Firstly, it was assumed that there is a link between a person’s height and their preferred desk height. This might not be a valid correlation – arm length or sitting height might give a more appropriate relationship. Or there might not be a reliable human measure to use in this instance.

Secondly, it was assumed that 20 mm is a suitable division for the buckets in Figure 15. It is possible that people in both the 1720–1739 mm and 1740–1759 mm buckets have exactly the same preference, and that 40 mm buckets would be appropriate. However, since Activity 8 showed that anything less than a 20 mm change didn’t make a noticeable difference, a 20 mm range in height seems quite reasonable.

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