This unit requires students to use statistics about the top ranked teams in the 2019 Rugby World Cup to predict the winner of the World Cup, justifying their prediction using data. Adaptations have been made for post the 2019 World Cup.
This unit requires students to use a data set containing statistics about the top ranked teams in the 2019 Rugby World Cup. Students will examine the variables and consider the attribute that each variable measures. They will compare groups (e.g. nations, positions) using technology to graph distributions and calculate measures. Finally, they will use their knowledge to predict the winner of the World Cup, justifying their prediction using data.
Students will carry out a statistical investigation using the PPDAC cycle (Problem, Plan, Data, Analysis, Conclusion). The data set of statistics about players in the rugby world cup, 2019, is provided. Students will need to work out which variables they will use to make their predictions about a likely winner.
Creating graphs of data also allows for ‘eyeballing’ the data to look for similarities and differences.
At the time this unit of work was updated (Nov 2020) the next rugby world cup event planned was the Women’s Rugby World Cup in 2021 (now delayed to 2022). When the original unit of work was created (September 2019) the upcoming rugby world cup event was the Men’s Rugby World Cup in 2019. Activities throughout the unit of work that use given data relate to either the 2021 women’s tournament or to the 2019 men’s tournament. Feel free to update the information to reflect the current (or next) rugby world cup.
Women’s Rugby World Cup 2021 https://www.rugbyworldcup.com/2021
The teams for the 2021 world cup are seeded based on their world rugby women’s ranking on 1 January 2020 (as this was the last time teams could play before COVID-19 pandemic).
The world women’s rugby rankings (November 2020) for rugby going into the 2021 tournament are/were:
This lesson and the remaining lessons use the 2019 Rugby World Cup data. Feel free to replace with current data.
In this lesson students explore tools that will be important to justifying their prediction about which team they think will win the World Cup. Use the Spreadsheet One.
For all the following investigative questions:
Investigative question One: What is the distribution of player positions?
The data from the spreadsheet is available in CODAP ready for students to use. Share the link with them – this could be through google classroom, teams or similar, just copy the link and share.
You may need to explain the positions to some students, e.g. fly half is often referred to as ‘number ten’ or ‘first five eighth’ in New Zealand.
Tell students: Using CODAP create two different graphs to show this data.
They are likely to make a dot plot and a bar graph. With the dot plot they can also include the count, see the dot plot in PowerPoint Two Slide 2. In CODAP the default organisation of categorical data is alphabetically. Students should be encouraged to rearrange the order to make more sense of the positions in rugby i.e. roughly ordering by jersey number, see the bar graph in PowerPoint Two Slide 2. This might make more sense when describing what the data shows.
Once students have created their graphs, they can make a text box in CODAP (or in word or google docs) and write 2-3 statements about what they notice about their graphs. Remind them to include the variable, the group (2019 RWC All Blacks) and if talking about numeric data (not this specific investigative question) to include values and units also.
After a suitable time gather the class to share the students’ graphs.
Which type of graph best answers the question, “What is the distribution of player positions?”
Both graphs provide answers to the question, but the ordered by position bar graph highlights differences in frequency better related to the position. For example, hookers and scrum half and fly half have the least, within the team these positions are single positions, whereas many of the other positions have two players e.g. lock, prop etc.
They also might note that there more forwards altogether than backs, 17 versus 14. They can reflect that there are more forward positions than back positions (8 versus 7) for example.
Which type of graph best answers the analysis question, “What fraction of the players are forwards and what fraction are backs?”
Investigative question Two: What are the weights of the All Black players?
Using CODAP display these data.
The default graph view of the data is shown in PowerPoint Two Slide 3.
Students can explore the data further by extending the x axis out (PPT 2 Slide 4) and/or by putting the data into bins and then fusing to make a histogram (PPT, Slide 5). (See Measuring Up for more on this). What statements can you make about the weights from these two displays?
What would the middle weight be? How could you find that out? (Show how to find the middle using CODAP – see Measuring up for full discussion on how to do this.) In CODAP you can add a movable value and add in count. Move the value until about half of the count is on each side of the value. This is the middle.
Formalise to showing the median. The median is an option in the ruler.
Are there any outliers? (Brad Weber, at 75 kg is light compared to the others)
Who do you think might be the heaviest player?
What is the range between the lightest and heaviest players?
In CODAP information about specific points can be found by clicking on the point.
In case card view when one dot is highlighted the specific “case” comes up. In the picture below you can see that the lightest player is highlighted and in the case card it says 1 selected of 31 cases and tells us that it is Brad Weber and gives all the data we have on Brad.
Explore the idea of finding the middle 50% as well using ideas from Measuring Up.
Investigative question Three: Do forwards tend to be taller than backs?
Students will have their own ideas about the answer to this question. Locks and loose forwards are the ball winners in the lineout so tend to be taller than players in other positions, which would support a hypothesis of forwards being taller than backs. With our data at the moment we cannot answer this question directly, we need to add in a new variable which tells if a position is forward or back.
We use CODAP and add a new variable. To do this we switch to table view and then click on the grey + on the right to insert a new attribute.
We name the attribute e.g. forward or back.
Instead of going through all 31 players, we can do a quick rearrange of the table and just rename for the eight positions. Drag the position attribute to the left and then the forward or back attribute so that they are hierarchal to the left in their own part of the table, see below.
Name each of the positions as forward or back. Then drag the attributes back into the main part of the table.
You can position the attributes where you like in the table by dragging the label.
Slide Six shows a dot plot with the data split by whether the position is a forward or a back. The median for each group has also been put in.
Do forwards tend to be taller than backs? They might notice that the data for the forwards is to the right of the data for the backs, i.e. the forwards tend to be taller.
What is the median height for forwards (read off graph – 1.89m)
What is the median height for backs (read off graph – 1.855m)
If we add a legend to our graph (PPT S7), and a bit of tidying up of the legend by dragging the positions about so they align with the colour position on the graph we can also explore the individual positions within the forwards and the backs and extend our response by asking the following analysis questions.
What positions have the tallest players? (As expected, the locks are the tallest, but loose forwards, and props are similar)
What positions have the shortest players? (As expected, the scrum halves followed by the fly halves are the shortest groups) The. th Students might notice that one of the scrum halves is quite a bit taller and wonder who that is. Click on the data point and they find out that it is TJ Perenara.
Investigative question Four: How are players’ weights related to their heights?
Relationship questions require looking for an association between two or more variables, in this case height and weight.
How could we display these data to look for a pattern?
Students may not be aware of scatterplots as a representation, but we can use CODAP to explore possible options. Ask students to make a graph with weight on one axis and height on the other, not dissimilar to what they have just done for height and forward or back. Suggest everyone puts the weight on the x axis and height on the y axis (so they are looking at the same graph).
Show them slide eight – Ask the students if they know what this type of graph is called?
If they do not know tell them it is called a scatter plot and it lets us see if there is an association between two numerical variables, in this case weight and height.
Is there any pattern in this graph?
We can look at the pattern in a scatterplot using the draw tool in CODAP. Click on the graph and then click on the camera icon and select open in draw tool. You then get an image of the graph that you can draw on. Select the line tool and draw in two lines, one that goes just above nearly all of the data and one that goes just below nearly all of the data. You might notice in the picture below that one data point is outside the lines. This shows the general pattern of the data, which in this case is showing that heavier All Blacks also tend to be taller and lighter All Blacks tend to be shorter. This is called a positive association and is all that students need to be looking for at this level.
By clicking on the outlying point we can see that Jordie Barrett is the person who appears to be quite a bit lighter than would be expected for his height. Students can also reflect on his position as an outside back and why this might be the case.
Students might also be interested in if the position they play is important so could drop the attribute forward or back into the middle of the graph. The following happens… PPT S10.
Students might note that forwards are generally heavier and taller than backs. They could guess as to who the back is that weighs over 110 kg and is over 1.95 m and click on the point to find that it is Sonny Bill Williams.
Investigative question Five: How are players’ total points related to their number of caps?
The point of this investigative question is to illustrate that there is often no clear association between variables. It makes intuitive sense to think that the more tests a rugby player participates in, the more points they are likely to score.
Slide 11 shows a scatterplot of the association between number of caps and number of points.
Is there a pattern in the points for this graph?
They should notice that generally the number of points is between 0 and 100 and the length of time playing does not necessarily mean more points.
Who do you think is the player who has over 600 points and about 75 tests?
What position do you think this player is? What might be one of their key roles in the game?
Click on the point to find that this outlier is Beauden Barrett who scored 617 points in 77 tests.
Why does playing more tests not necessarily lead to more points?
Students who are familiar with rugby will know that most points are scored by the fly halves, who tend to be the goal kickers.
Again, we can add in another variable, e.g. position into the graph to see if it gives us anything else we can discuss about the data. This is the flexibility that using technology and software such as CODAP allows us. See PPT2 S12.
In this lesson students are encouraged to come up with a prediction about which team will win the World Cup. It is important that they use evidence, related to the variables in the data set. Note: the 2019 Rugby World Cup has gone, the data provided is for teams that were in the 2019 Rugby World Cup. You can use this data but base it on the six teams going into a tournament that we are yet to know the outcome of. Alternatively, if it is a world cup year, switch the data for the latest data from the six countries.
In this lesson students are the consumers of others’ reports and are expected to use statistical literacy to evaluate the validity of findings. From the outset it is important for students to understand that there is ‘no one correct answer’ and that different choices and combinations of variables may lead to different predictions.
PowerPoint Four has an example of a report. Focus on the questions for discussion in the speech bubbles. Pay attention to justification, and sensible use of technology to present the data.
Printed from https://nzmaths.co.nz/resource/rugby-world-cup-stats at 6:42am on the 20th January 2022