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Level Three > Statistics

Sports

Purpose:

This week we collect data about sporting activities and present the data using stem-and-leaf graphs and bar charts.

Specific Learning Outcomes:
• display data in bar graphs and stem and leaf graphs
• discuss features of data display using middle, spread, and outliers.
Description of mathematics:

Planning an investigation at this level is more complex than at Level 2. Here the students can begin to talk about situations they have experienced, pose questions and produce a plan for a statistical investigation. Students may be capable now of incorporating a computer into their work. In this unit the students are introduced to stem-and-leaf graphs, and use bar charts to display data. Depending on the nature of the questions they are posing, they will find out that they need to collect and organise the data in different ways. When considering the data they now start to see and talk about distinctive features of their displays such as outliers and modes.

A stem-and-leaf graph is a bar graph made by arranging numerical data in a display. The first part of the number is the stem and the last part is the leaf. Data displayed in this way makes finding the range, mode and median (middle number) relatively easy.

Data: 12, 14, 17, 25, 36, 38, 40, 41, 43

Required Resource Materials:
Prepared stem and leaf graph.
Stop watch.
Calculators.
Key Vocabulary:

back-to-back stem-and-leaf graph, decade, cluster, data sets, middle, outliers,

Activity:

Session 1

We begin the week by looking at our resting pulse rate and our pulse rate after we’ve done some exercise. We display this data in a back-to-back stem and leaf graph.

1. Pose the problem: How many times will your heart beat today?
2. Ask the students to indicate whether they think it will beat more than thousand/ more than ten thousand/ more than a million.
3. Discuss ideas that the students have for working out the answer. List these ideas on the board, for example:
need to know the number of beats per minute and then the number of minutes in a day
– need to consider that our heart beat changes
4. Ask the students to plan a way of finding how many times their heart beats in a minute.
5. Share plans, for example:
- Work with a partner who tells you when a minute has passed (using the second hand on the class clock).
- Work with a partner. Count the beats for 15 seconds and then multiply by 4.
6. Draw a stem-and-leaf graph on a chart or the board

7. Have a student tell you their resting pulse (76). Place it on the graph without explaining how you positioned it. Ask another student to tell you the pulse rate and put it on the graph. Again don’t give an explanation.
8. Then ask the students:
Can anyone explain why I’ve put those numbers at that place on the graph?
Discuss the ‘tens’ digit as the stem and the ‘ones’ digit as the leaves.
9. Now get the students to add their pulse rates on the graph. If the students have not put the ones digits in order then this needs to be discussed and then changed.
10. Look at the stem-and-leaf graph and discuss.
Which is the most popular decade?
Could you tell without counting the number of digits on each leaf?
(This is where the similarities between stem-and-leaf and bar charts can be made.)
Which pulse is near the middle? (Stem-and-leaf graphs are great for answering this question as you can count in from either "end" of the data)
Which pulse rates are grouped together in clusters?
Which pulse rates are lying outside the cluster?
11. Discuss the factors which cause pulse rates (heart beats) to vary.
12. Now send the students out for a two minute fitness run. Take their pulse again and put the figures on the other side of the graph. Get the students to make statements about the data they collected;
Are there any surprises?
What are the differences between the two sets of data.
Get the students to make observations about data in the middle, spread and outliers.
13. At the end of the session reflect back on the initial problem about heart-beats in a day. Leave this as a problem for the students to work on during the week.

Session 2-3

Over the next two days the students gather information around the theme of sports. They display and share the information using stem-and-leaf graphs or other displays they have previously studied.

1. Brainstorm ideas for sports investigations. List these on the board. Some ideas could include;
How many crunches (sit ups) they can do in a minute?
How many breaths they take in a minute before exercise, after exercise?
How long it takes to run a certain distance (time in seconds)?
How many skips in a minute?
2. Look at the list of ideas and discuss the ones that would be suitable for display as a stem-and-leaf graphs.
3. Let the students work in pairs or small groups to plan and then conduct an investigation. Have them consider the practicalities of data collection.
4. Discuss with students the features that you want them to include in their report of the investigation. The reports could include:
- The aim of the investigation.
- A description of how the data was collected.
- A data display
- A written summary about the data making use of middle, spread and outliers.

Session 4 - 5

In these two sessions we focus on the use of bar charts to display the results of our "equipment" surveys

1. We begin this session asking the students which activity they like doing at lunchtimes. We list the possibilities on the board.
2. Discuss ideas for quickly deciding which is the favoured activity. These could include:
- Standing in lines under each activity
- Putting a tally mark under each activity
- Putting a post-it tag under each activity
3. Discuss ideas for making a permanent display of the data. As a class make a bar chart with each student placing a coloured square with their preferred activity.
4. Look at the bar graph. Are there any surprises in the data we’ve collected? What can you say about the information in this graph?
5. Tell the students that the principal has asked the class to find out which equipment the school should buy for lunchtime activity. (A letter from the principal or a request in person would be better still.)
6. Get small groups of students to investigate a particular area (cricket gear, rugby balls, board games, library books etc) and put the information on a bar graph. The equipment can then be "matched" with the survey about the students’s preferred activity.
7. They will then give recommendations to the school principal (write letter, give presentation, e-mail) for increasing or decreasing the equipment available to the students at lunch time.

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