Comparing sets of data - BBC Bitesize

Key points

An image of two sets of data. The mean, median, mode, and range have been calculated for each set. — Image caption,
Understanding mean, median, mode and range is essential to be able to compare sets of data.

An understanding of , , and is essential to be able to compare sets of data.
Data can be compared in two different ways:
1. By comparing an , such as the mean, median or mode. An average gives a typical value, so comparing averages shows whether one set of data is generally higher or lower than the other. The mean is the most common way to compare two sets of data, but the median or mode may be better if there is an in the data.
2. By comparing the . The range shows how spread out the data is, so comparing ranges shows whether one set of data is more than the other.

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How to compare data sets

To compare two or more data sets, it is too complex to look at every value, especially if there are a large number of figures. It is easier to compare the data using one typical value to represent each data set, such as the , or . This helps to suggest which set of data is higher on average.
The is the difference between the lowest and highest values. It measures how varied the data is. If a set of data has a lower range, the values are closer together and so the data is more consistent.

Examples

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Two farmers grow 8 marrows. These are the lengths of the marrows in cm.
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One way to compare the two sets is to calculate the average of each group. The mean is a sensible average to use here because there are no outliers (unusually high or low results) that would affect the answer. To calculate the mean, add the values, then divide by how many values there are. Set B has a higher mean than set A. On average, Farmer B grew longer marrows.
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Another way to compare the two sets is to calculate the range of each group. The range is not an average. The range is the difference between the lowest and highest values. The range of lengths from Farmer A is 16 cm. There is 16 cm between Farmer A’s shortest and longest marrow. The range of lengths from Farmer B is 11 cm. There is 11 cm between Farmer B’s shortest and longest marrow.
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The range shows how spread out the data is. A higher range means the values are more varied. 16 cm is a wider range of lengths than 11 cm. Therefore, Farmer A’s marrows were more varied in length. When the values are more spread out, the data is said to be less consistent.
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These are the finishing times of students in a race, in seconds. To compare the times of the two classes, consider the average and range of each set of times. There is an outlier in class B of 50 seconds. When there are outliers in the data, it is better to use the median as a measure of average instead of the mean. This is because the outlier would increase the mean and would therefore not represent a typical time. The median is not affected in the same way.
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To calculate the median, find the middle number in the ordered lists. Class B has a higher median than Class A. This means on average, Class B were slower than Class A. Note that a higher average is usually not a good thing when thinking about times in a race - Class A had a lower median time so Class A were quicker and performed better on average.
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To calculate the range, subtract the lowest value from the highest value. Class B had a higher range than Class A. This means that Class B’s times were more varied. Another way to say this is that Class B’s times were less consistent as their times were more spread out.
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Follow these six steps to compare two sets of data, A and B. 1. Calculate an appropriate average for both sets. The example above uses the mean. It may be more appropriate to compare medians or modes. 2. Say which average is higher. 3. Link this to the context of the data using words such as better, slower, longer or taller. Look at the next slide to read the last three steps.
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4. Calculate the range for both sets. 5. Say which range is bigger. 6. Describe the spread of the data by using the terms ‘varied’ or ‘consistent’. A higher range shows a set of results that are more spread out and less consistent.

Match the comparisons with the statements

Practise comparing data with this activity. Match the comparisons with the correct statement.

Question

Alex and Tia have completed eight spelling tests and their ordered results are below. Each student wants to argue they have performed better.

What average could each of them use to suggest they are better at spelling?
Could the range be used as evidence too?
Whose argument would be most convincing?

An image of two sets of data. Each set of data is made up of eight values. The first set of data is labelled, Alex, and has values, seven, comma, ten, comma, twelve, comma, fourteen, comma, fifteen, comma, sixteen, comma, seventeen, comma, seventeen. The second set of data is labelled, Tia, and has values, thirteen, comma, thirteen, comma, fifteen, comma, fifteen, comma, fifteen, comma, sixteen, comma, sixteen, comma, seventeen.

Practise comparing sets of data

Quiz

Practise comparing sets of data with this quiz. You may need a pen and paper to help you.

Real-life maths

An image of a statistician working at a computer. — Image caption,
Statistics may be carefully chosen for content in the media.

Statistics and averages are often presented in the news, in documentaries or on social media.

Different averages can be used to support a particular point of view. Statistics may be carefully chosen for content in the media to make an argument or present a certain way of thinking to an audience.

By selecting a particular average to compare figures, it is possible to influence other people's opinions.

As a reader or viewer, a clear understanding of averages is helpful to spot when data may be presented in a way that is potentially misleading.