Succeed with maths – Part 2
Succeed with maths – Part 2

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

Free course

Succeed with maths – Part 2

2 Measuring the spread of a data set

As well as finding a typical value or average for a set of data, it is also useful to see how the data values are spread about the typical value. Here’s an example to start exploring why this is.

Last year, Sam grew two varieties of sunflowers and measured the heights of the flowers in inches. Here are Sam’s results:

Table _unit8.3.1 Table 7 The heights of Sam’s sunflowers shown in inches

Variety A 60 59 66 55 55 62 58 65
Variety B 52 69 61 60 54 67 50 67

Sam wants to compare how each sunflower variety performed based on height, so wants to look at the data in more detail.

Activity _unit8.3.1 Activity 5 How tall are the sunflowers on average?

Timing: Allow approximately 5 minutes
  • a.Find the mean height of the sunflowers of variety A.

Answer

  • a.Mean height variety cap a equation sequence equals sum with, 8 , summands 60 plus 59 plus 66 plus 55 plus 55 plus 62 plus 58 plus 65 divided by eight equals 60 inches
  • b.Find the mean height of the sunflowers of variety B.

Answer

  • b.On average, the sunflowers of the two varieties are the same height: 60 inches.

When Sam looked at the sunflowers, they did look about the same height on average, but there was still a difference. To investigate this difference have a look at the heights plotted on number lines in Figure 3.

Figure _unit8.3.1 Figure 3 Number lines, showing sunflower heights

The blue dots represent the heights in inches of the sunflowers of variety A, and the red dots represent the heights in inches of the sunflowers of variety B. You should be able to see that the red dots are more spread out than the blue dots. This means that heights of sunflowers of variety A are more consistent (closer together), than the heights of the sunflowers of variety B, which are more variable (more spread out). If you had only looked at the mean value this would not have been evident. This shows how useful it is to look at the spread of data as well as the average.

One way of measuring the spread of a data set is called the range. The range is calculated as follows:

Range of data set = largest value – smallest value

For the sunflowers of variety A, the smallest value is 55 inches and the largest value is 66 inches.

So the range for variety A = 66 – 55 = 11 inches

The smallest value in the data set for variety B is 50 inches, and the largest value is 69 inches.

So the range for variety B = 69 – 50 = 19 inches

So even though both sunflower varieties had the same mean height, there was much more variation – that is, a wider range – of heights seen in variety B compared to variety A. If you grew sunflowers commercially, knowing this about a particular variety would be very useful at harvest time!

The range gives an idea of the spread of the data, although it can be affected by either very high or very low values. There are other ways of measuring the spread of a data set, and you’ll meet these if you continue studying mathematics or statistics.

The next section gets you thinking about what questions to ask when you are presented with averages

Skip Your course resources
SWMB_2

Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to University-level study, we offer two introductory routes to our qualifications. You could either choose to start with an Access module, or a module which allows you to count your previous learning towards an Open University qualification. Read our guide on Where to take your learning next for more information.

Not ready for formal University study? Then browse over 1000 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus371