Year 10 – Maths – Using data

There couldn’t be a better time to delve into data and think about how we use it. This post goes through different ways to process and represent data, covering averages, pie charts, scattergraphs, boxplots and cumulative frequency. It will focus on trying to make sense of data by using reasoning skills to help you interpret statistical information.

Averages

If you need a reminder of how to work out each of the three averages (mean, median and mode) and the range have a look through the Analysing data section on BBC bitesize here. Then try the three questions below:

In this task the different averages are compared to consider how useful each is in one situation:

The following four problems all involve the mean average, but they require you to think quite carefully about how you can work out what’s needed.

Hint: In these problems it is often helpful to work backwards from the mean to work out the total.

In this Growing families NRICH task, information is provided in a table. The first question is fiarly straightforward to work out but the second, seemingly quite harmless question is actually a real challenge.

Pie charts

The first activity is about different cereals.

Work out what the missing numbers are (the green cells). Then match each of these five cereals with the correct pie chart below.

The pie chart below shows the proportions for another cereal called Banana Flakes.

Copy and complete the table with your estimates.

Percentages are often used with pie charts because it is a visual representation of parts making up a whole.

Three students, Hannan, Rachida and Sharon made their own dice out of paper. They each tested their dice to make sure they were fair. These tally charts show their results after 50 throws. Complete the frequency in Sharon’s table.

Each student displayed their data on a bar chart, and a pie chart. They gave in their charts but forgot to write their names on them. Which bar chart and which pie chart belongs to each student?

Which two of these dice would you use for a fair game? Explain how you decided.

Now try testing your own dice by rolling it 50 times and try drawing a bar chart and pie chart of your own results. How fair is your dice compared to Hannan, Rachida and Sharon’s? If you can’t make your own dice or don’t have one at home, you can use an online dice instead. Send your work in to the Student Showcase.

Scattergraphs

Below are some notes explaining some of the terminology associated with scattergraphs. A scattergraph is used to find out whether there is a relationship between two pieces of data rather than to compare two sets of data of one type – for that you might use averages or dual bar charts, box plots or histograms.

Notice that some of these terms are different to the ones you might use in science. For example an outlier would often be called an anomaly in science.

In Bees, practise plotting scattergraphs in order to find out more about the honey bee and its behaviour. This is a good example of data helping to better understand an issue and how conservationists or other scientists might make use of data.

Boxplots

Work through the key ideas about boxplots using the CIMT tutorial here. It includes an introduction and some examples but if you need more explanation, watch this Corbettmaths clip.

In this Temperatures task, data is provided in the form of a time series graph that is then converted into boxplots:

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When you compare the boxplots try to make a statement about a particular statistic for the two teams and put that into context as well, ie say what that means about their javelin throws. You should do this for two different statistics if you can.

If you also study Statistics GCSE you need to interpret boxplots in this same way, but in addition you may also need to compare the symmetry or skew of the two distrubutions.

Cumulative frequency

The word cumulative is an adjective that means something is building up or being added to. See how this works in the grouped frequency table below – note that the important aspects in the second table are highlighted.

Hint: Since there are 80 students in total, the median will be at 40 (or 40.5)

To go through how to plot and read values from a cumulative frequency graph, go through these slides:

Now practise these skills in order to solve the following problem. If you haven’t got graph paper you can print some here.

Further ideas

There is a famous, widely used quote “There are three kinds of lies: lies, damned lies, and statistics”. Watch this talk Lies, Damned Lies and Newspapers by Dr Emily Grossman.

Data is used so widely in the media and in politics now, that sometimes it is more helpful to go back to the underlying facts of any story. Full Fact is an independent fact checking charity – visit their website here.

If you are interested in the statistical analysis and mathematical modelling that has been discussed recently, The Coronavirus Curve clip by Ben Sparks from Numberphile takes us through the maths of it. This involves some quite advanced maths, but the Further Maths Certificate does cover differentiation).

Or if you are interested in the work of football statisticians watch this one:

ANSWERS – click below

Averages

You can find the Growing families solution here

Pie charts

Scattergraphs
Boxplots
Temperatures – solutions
Two statements such as: Similarities: January has the lowest temperature in both states. June and July have the greatest temperatures. Temperatures increase from the beginning of the year to the middle of the year, then decrease again. Differences: California’s temperatures are higher than Washington’s for every month. The range of temperatures is greater for California than for Washington.
B
Lowest temperature is 45º and highest is 69º.
D
March, April, May, June, September, October, November The temperatures are between 68º and 92º.
  • Boxplots comparisons:
  • The green team’s median is higher than the blue team’s median. This means that, on average, the green team threw the javelin further than the blue team.
  • The interquartile range for the green team is equal to the interquartile range for the blue team. This means that the throws from the two teams were equally consistent.

Cumulative frequency