Texting Olympics

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Purpose

This is a level 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

Achievement Objectives
S4-1: Plan and conduct investigations using the statistical enquiry cycle: determining appropriate variables and data collection methods; gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends; comparing distributions visually; communicating findings, using appropriate displays.
S4-2: Evaluate statements made by others about the findings of statistical investigations and probability activities.
Student Activity

      

Click on the image to enlarge it. Click again to close. Download PDF (1467 KB)

Specific Learning Outcomes

create a stem and leaf graph

critique conclusions

interpret information from a graph

create a scatter plot

 

Description of Mathematics

This diagram shows the areas of Statistics involved in this activity.

stats diagram.

The bottom half of the diagram represents the 5 stages of the PPDAC (Problem, Plan, Data, Analysis, Conclusion) statistics investigation cycle.

Statistical Ideas

Texting Olympics involves the following statistical ideas: using the PPDAC cycle, multivariate data sets, stem-and-leaf graphs, scatter plots, and histograms.
The activities in Texting Olympics are good examples of ways to use multivariate data sets. Students at this level need to experience exploring statistics using more sophisticated techniques than those used with simple category or univariate data.

Required Resource Materials
The texting time results (see copymaster)

Stopwatches

A computer spreadsheet/graphing program (if available)

FIO, Levels 4 -4+, Statistics in the Media, Texting Olympics, pages 1-4

A classmate

Activity

Activity One

Before the students start the activity, it may be useful to have them collect their own data relating to the Texting Olympics. Doing this will raise questions regarding the logistics of the data collection process and will make it easy for them to answer question 1. The class data can later be graphed in the same way as the graphs produced for the supplied data and then compared. (Note: The data in this activity is real and was collected from year 9 students [names changed]. Also note that 1:54.94 is one way of recording 1 minute, 54.94 seconds. Watch for students who get confused by the “out of 60” for seconds and the “out of 100” decimal notation for part-seconds.)
For question 2, decide if you want the students to work out the seconds manually or whether, if computers are available, you want to challenge them to explore formulae to do the task for them. If they are to do the data conversion (and later, the graphs) on the computer, it would be sensible to have the data available for them as a spreadsheet file rather than each student entering the data separately. (Although this activity is particularly suited to the use of computers, students without that access can still make the required graphs, although the one for Activity Three, question 1a may need to be simplifi ed, as suggested later.)
The process of turning minutes into seconds in this activity is necessary before the students can analyse results and make graphs.
A stem-and-leaf graph, as shown in question 3, is an excellent way for the students to display the data as they organise it. Encourage them to realise that it is more efficient to put the “leaves” into the graph in the order they appear in the raw data than to try to order the data before drawing up the graph, as they may otherwise miss some data out. However, as suggested in the student book for this activity, it is usually best to reorder the leaves of the stem-and-leaf graph into numerical order before the display is used for analysis.
Question 4 requires the students to analyse a different sort of graph (in this case, a histogram) based on the same data. The idea of making different graphs with the same data is that, sometimes, by regrouping the data you get a different or a more useful display. In this case, the intervals for the histogram are 2 seconds,
whereas the stem-and-leaf graph, necessarily, has 1-second intervals. With a histogram, individual values are less visible, so the graph is more abstract. You could discuss the usefulness of each type of graph in the Texting Olympics context.

Activity Two

You could start with a discussion as to why the students in the data set provided were comparatively better in hurdles. This discussion may lead to new investigative questions. Your students may wish to repeat the investigation with different people doing different events first to see if results are similar.
If students struggle to understand how the scatter plot works, have them plot some points by hand. If they timed themselves for these events (as suggested in the notes for Activity One), they could locate where their own results would be placed.

Activity Three

Although this activity can be done by hand, the students will fi nd it much easier to use a computer spreadsheet program, especially if they have already entered the data for Activity One, question 2 into a spreadsheet. A stacked bar graph, as shown in the Answers, clearly shows the order of the students overall, and you can also see where individual event times were faster or slower. (Students without computer access
could make a stacked bar graph by hand, but it might be simpler if they just added up the 3 times for each student and then put all the total times in order.)
The different way of selecting a team proposed in question 2 should lead to some interesting discussion and help the students to realise that data can be analysed in different ways, each of which will have advantages and disadvantages.

Investigation

Whenever students do statistical investigations, it is important to revisit the PPDAC cycle. Students tend to have most diffi culty in converting from an idea or problem to a statistical question. The planning phase is arguably the most vital. Students need to decide what they will measure and how they will measure it.
 

Extension

Students could:
• do a parallel investigation activity with real athletic events.
• investigate how long they can balance on their right foot and then on their left foot (or other timed activities).
• investigate the links between typing speed and cellphone texting speed or texting speed to cellphone bill size – the possibilities are endless!

Answers to Activities

Activity One
1. Details to sort out will vary. For example, they
could be based on these questions:
• Can I have a practice first?
• I’ve never had a cellphone. Can I get extra time?
• How will the timer know the exact second I finish?
• Can I set up my phone ready to text to someone?
• Can we use predictive text? (Predictive text [when the cellphone predicts the word or words you want to use from some of the keys you press] can vary from phone to phone – for example, newer models have more advanced methods, so it would be fairer if no one used this feature.)
• Most people our age use texting language, so can we use it in the marathon? (People invent various short cuts for texting [for example, “c u l8r” for “see you later”], and although they usually make sense, it would be very hard to
judge because there are different forms of the same words and some would take less time than others. Also, what makes sense to the person doing the texting may not make sense to the reader.)
2.

results table.

3. a. A graph with the part-seconds in order would look like this:

graph.


b. To win a sprint, you need to have the fastest time. The fastest time is 4.0 seconds, which was Toline’s. There were 5 times below 5 seconds: 4.0, 4.1, 4.3, 4.7, and
4.8. This is of the class. Quinten wants to include the 3 students who were timed at exactly 5 seconds. But 8 out of 30 is more than , and calling that many students “champions” makes the description less meaningful.
4. a. Possible observations are:
• Very few students: took more than 14 seconds to do the sprint took between 10 and 12 seconds to do the sprint.
• Almost half the students: took between 4 and 6 seconds to do the sprint
took between 6 and 12 seconds to do the sprint.
• No students: took less than 4 seconds to do the sprint took between 14 and 16 seconds to do the sprint.
• Most students: took more than 5 seconds to do the sprint took between 4 and 8 seconds to do the sprint.
• More students took between 4 and 6 seconds to do the sprint than for any other time interval.
b. Opinions will vary. The stem-and-leaf graph gives more information than the histogram. The histogram summarises the data more, and individual values are no longer apparent. Gaps and peaks are probably more obvious in the histogram.

Activity Two

1. a. Rebecca and Koria
b. A possible graph is:

graph.
2. a. Koria, Aki, Aoife
b. Possible choices are:
• Much better in marathon than hurdles: Quaid
• Much better in hurdles than marathon (although not necessarily very good at either!): Aki, Aoife, Abhay, Andrew, Susan, Chris, Koria, Aketu
c. Mary
d. Mary, Siri, Tariq, Toline, Ming, Rebecca
3. Generally, students with fast marathon times have fast hurdle times (see 2d).
 

Activity Three

1. a. A fourth column, sorted to show total time in order for all the students, would
be:

time order.

A stacked bar graph showing the data (from longest to shortest time) for all the students could look like this:

stacked bar graph.

b. Mary, Siri, Toline, Tariq, Ming
2. a. Mary, Toline, Ming, Tariq, Siri
A points table in order for the people who scored points under Quinten’s system would be:

points table.

For this class, the team of 5 remains the same, although the order changes.
b. Advantages and disadvantages of each system:
Taylah’s system generates the better all-round candidates and has more potential to get an overall winner in a gymnastics-style competition or “triathlon”. Quinten’s system highlights those who are very good in single events and has more potential to generate a gold medal in an individual event.
c. Decisions will vary.
Under Quinten’s system, the 6th person (the reserve) would be Yvette, who did very well (3rd) in the sprint but poorly in the other two events.
Under Taylah’s system of total time, Rebecca (as 6th) would be the reserve, with a total time only 4.2 seconds less than Ming’s.
 

Investigation

Investigations will vary.

Key Competencies

Texting Olympics can be used to develop these key competencies:
• thinking: justifying and verifying, discerning if answers are reasonable, exploring and using patterns and relationships in data, and designing investigations
• using language, symbols, and texts: interpreting statistical information, communicating findings, using ICT as appropriate, interpreting visual representations, and demonstrating statistical literacy
• relating to others: sharing ideas.
 

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Level Four