Averages and range
The Land Rover BAR team analyse data to help them increase performance. Challenge your students on averages and range to see if they have what it takes to join the team.
You could begin the lesson by asking students to recall prior arithmetic knowledge with addition and division, including with decimals (allow use of a calculator where appropriate). Introduce the topic and why we need averages in real life: basing decisions on just one statistic at one time is unreliable. For example, deciding whether a football team is doing well based on one match is not as meaningful as looking at the whole season’s results.
You could include a practical activity within the lesson. Ask students to create their own table of data with variables – heart rate, number of star jumps, for example – and calculate averages. If they have learnt about scatter graphs already, then correlation could be tied in with this. Depending on their level students could use ungrouped or grouped data.
Finish the lesson by presenting students with average speeds, heart rates and so on and generate data which would satisfy those answers. They could also decide whether that average was best achieved with the mean, mode or median.
Further ideas/ STEM club ideas
Students could look up longer distance races and explore these using IT to work out average performance for different boats. This could be extended to look at America’s Cup races through history and use averages to understand how boat design and performance has advanced through time. If they were learning to code in STEM club, they could tie this in.
KS3 NC Mathematics - statistics
- Describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)
- S2 interpret and construct tables, including frequency tables
- S4 interpret, analyse and compare the distributions of data sets from univariate empirical distributions through: appropriate graphical representation involving discrete, continuous and grouped data; appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers)
- S3.3, S3.3h Calculate median, mean, range, mode and modal class from lists and tables of data
- S4.4 Compare distributions and make inferences
- D2.2, D3.3 Calculate the mean, median, mode and range of discrete data.
- D5.2 Use and interpret the statistical measures: mode, median, mean and range for discrete and continuous data, including comparing distributions.
- D6.3 Identify the modal class of grouped data. Calculate the mean of grouped discrete data.
- D7.2 Calculate the mean from grouped continuous data.
- Find the mean, median, mode and range from grouped frequency tables
- Find the mean, median, mode and range from ungrouped frequency tables and explain why it is an estimate
- Use mean, median, mode and range to compare two distributions (continous and discrete data)
- Interpret diagrams and graphs to compare sets of data
- Examine results critically, select and justify choice of statistics recognising the limitations of any assumptions and their effect on the conclusions drawn
- Use the mean, median, mode and range from grouped frequency tables to compare distributions
- Calculate the upper quartile, lower quartile and interquartile range of a set of discrete data and use them to describe a data set
- Recognise and use the most appropriate data to compare distributions
Fourth level Numeracy & Mathematics:
- Compare numerical information in real life contexts by finding the mean, median, mode andrange of sets of numbers. Decide which type of average is most appropriate to use and discuss how using an alternative type of average could be misleading.
- Select appropriately from a wide range of tables, charts, diagrams and graphs when displaying discrete, continuous or grouped data to clearly communicate the significant features of the data
KS3 Using Mathematics
- Collect and record discrete and continuous data using a variety of methods;
- Construct and interpret a variety of diagrams and graphs for discrete and continuous data;
- Work out and use the median and mode;
- Work out the mean, median and mode of a frequency distribution;
- Use one of the measures of average to compare two sets of data.
- Calculate median, mean, range and mode, and understand their uses;
- Interpret a wide range of graphs and diagrams and draw conclusions.