Lesson 3 Working with Outliers
Teacher Advice
Goals of Lesson
To understand how data about past trends may help predict future performances.
To understand the concept of how real data is likely to contain ‘outliers’ and hence that graphical representations should be lines of best fit, not connecting every point.
Features of the Lesson
Pupils consider how they may use the pattern of progression of performances to predict what may happen in the future.
Pupils discover the difficulties in modelling real (imperfect data) and the concept of outliers.
Pupils consider outliers and produce a line of best fit for their graph and use this to make predictions about future performances.
Summary
Part 1: Making predictions requires graphical data Pupils consider how they may use the pattern of progression of performances in their chosen event to predict what may happen in the future. (15 minutes). |
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Part 2: Using trend lines of best fit Teacher introduces concepts of lines of best fit, extrapolation and outlier data. (15 minutes). |
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Part 3: Constructing and using scatter plots and trendlines Pupils use the notion of scatter plots, and lines of best fit and extrapolation to address their questions about the future. (20 minutes). |
Preparation
Copies of the 800m track data plotted as a scatter plot.
Graph paper for pupils
Preparation of assessment rubric from information collected in lesson two.
Picture of the 1896 stadium
Prior Learning for Lesson 3
Pupils should be familiar with the following concepts:
Scatter plot
Linear relationships represented in tabular and graphical forms
Interpolation and extrapolation on graphs
Part 1: Making predictions requires graphical data (15 minutes)
Pupils frame questions about predicting future events and build a need for graphical representation of their data in order to do this (15 minutes).
Activities |
Teaching and Learning Notes |
Key question:
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Now that pupils have a more conclusive understanding about whether or not women have improved faster than men, pose the question to them, “What other questions may we ask from this data?” Direct their attention to using the data to predict future performances. As a class, generate a list of possible questions. (see: TL11: Using data to predict future events for a possible list). Allow the pupils to select the question of most interest to them. |
Key question
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Provide pupils with the opportunity to return to their groups and use the tabular data, to try to answer this question. Discuss with pupils the point that up to now, data has been represented in tabular form and help pupils to see the limitations of tabular data when analysing trends and extrapolating beyond the data in the table. If time is a problem, you could delete asking pupils to try and answer their question using tabular data and just point out why this is hard and how graphical representation can help. |
Key question
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It is worth asking what other ways data can be represented, but be prepared to direct pupils' attention to the need to represent the data in graphical form. A quick whiteboard sketch showing how graphical lines can be extrapolated will be helpful see TL11. |
Part 2 Using trend lines of best fit
Pupils work with data on the 800m to build understandings of lines of best fit, extrapolation and outlier data (15 minutes)
Activities |
Teaching and Learning Notes |
Key questions
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Hand out the scatter plot of the time series data for the 800m and ask why connecting every point is unlikely to be helpful. Call for comments about points that do not seem to fit in the men’s or women’s data and use this to introduce the concept of outliers. See: TL12: Outliers for further detail. TL7 contains background information (and a photo), explaining why the 1896 event was a huge outlier. TL5 includes discussion on some reasons for outliers in other events. Show or have the pupils draw trend lines of best fit that ignore outlier points. Discuss with pupils how these points may be considered and/or ignored in generating a line of best fit. (See TL13: Linear vs non-linear graphing for advice about modelling a non-linear graph). |
Key question:
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Have pupils use their trendlines for the 800m event to answer prediction questions about that event – such as whether it seems women will eventually overtake men. |
Part 3: Constructing and using scatter plots and trend lines
Pupils use the notion of scatter plots, and lines of best fit and extrapolation to address their questions about the future. (20 minutes)
Activities |
Teaching and Learning Notes |
Key Question:
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Allow pupils the opportunity to generate lines of best fit for their scatter plots. Visit each group and ask about any outlier performances within their event and what reasons they may have for these performances. TL5 and TL7 provide teachers with some information on outliers.
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Key Question:
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Some groups may want to use non linear trend lines (see TL13 for discussion of this issue).
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Homework:
For homework pupils produce a final draft of the work they have completed in the Case using the ‘enquiry process’. As part of this, they should research their event for some interesting data about outlier performances that might explain why they had outliers.