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Walking tall?

This is a level 5 statistics activity from the Figure It Out series. It is focused on constructing a bar graph on a computer, interpreting data from a graph, evaluating a hypothesis from the data, planning an investigation, and collecting and displaying data. A PDF of the student activity is included.

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Tags

  • AudienceKaiako
  • Learning AreaMathematics and Statistics
  • Resource LanguageEnglish
  • Resource typeActivity
  • SeriesFigure It Out

About this resource

Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.

This resource provides the teachers' notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.

Specific learning outcomes:

  • Construct a bar graph on a computer.
  • Interpret data from a graph.
  • Evaluate a hypothesis from the data.
  • Plan an investigation.
  • Collect and display data.
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    Walking tall?

    Achievement objectives

    S5-1: Plan and conduct surveys and experiments using the statistical enquiry cycle: determining appropriate variables and measures; considering sources of variation; gathering and cleaning data; using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets; comparing sample distributions visually, using measures of centre, spread, and proportion; presenting a report of findings.

    S5-2: Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings.

    Required materials

    • Figure It Out, Level 4+, Statistics, Book two, "Walking tall", page 8
    • a calculator
    • a computer

    See Materials that come with this resource to download:

    • Walking tall activity (.pdf)

    Activity

     | 

    In this activity, students investigate a hypothesis by comparing data obtained from two different groups. They learn that as a general principle, when comparing data from samples of different sizes, they should use percentages rather than raw data.

    When they look at the graph they have created for question 1b, your students should recognise that it is difficult to compare the two sets of data because the number of students in each group is very different. When they convert the frequencies in each interval to percentages and graph these percentages (in questions 2a–b), they can make comparisons more easily.

    To do question 2, the students need to extend their spreadsheet and create a graph using columns 1, 4, and 5. Note that the values given in the students’ book have been rounded to 1 decimal place, which is fairly standard for percentages. To do this in the spreadsheet, select the cells that contain the numbers to be rounded, click on Format on the menu bar, choose Cells, then the Number tab, and finally, select “Number” from the list of alternatives. Change the number in the small “Decimal places” window to 1.

    Encourage your students to use a formula to convert the raw data to percentages. The following spreadsheet shows how this can be done using =B2/B$9*100. Note the “$” that has been inserted into the B9 cell reference. This lets the program know that the value found in cell B9 (in this case, the total number of boys who walk or bike) is a constant (that is, it remains the same in all calculations using this formula).

    Excel spreadsheet titled 'Walking Tall'. Data shows height, boys who walk or bike, boys who use a bus or car, percentage of all walkers and bikers, and percentage of all bus and car users.

    Use the cursor to grab the bottom right-hand corner of cell D2 and drag it down the next 7 lines. Release the mouse button, and the maths is done! Use a similar process to complete the last column.

    If you want to select cells from non-adjacent columns (which can be important when graphing just part of the data in a spreadsheet), select the first group of cells you need, hold down the CTRL key (or the Apple key, if using a Macintosh) and select whatever other cells are required.

    Question 3 may be the first time that your students have encountered the use of a hypothesis as the basis for a statistical investigation, so discuss the concept with them. When developing a hypothesis or framing a question, they should think about the kind of data they would need to collect in order to prove or disprove it and how they would use that data to reach a conclusion. The following is a useful framework for an investigation.

    1.

    Clarify the hypothesis or question. Ask:

    • What is the investigation really about? Can I break it into steps?
    • What information do I already have, and what further information do I need?

    2.

    Devise a strategy for the investigation. Ask:

    • Where can I find the data I need? How will I gather it? What resources or equipment do I need?

    3.

    Carry out the plan. Collect data, make calculations, and create suitable graphs.

    4.

    Draw conclusions. Analyse the calculations and graphs, outline the findings, and give an answer or conclusion to the investigation.

    5.

    Report back. This can be done in verbal or written form and may include tables, charts, and displays.

    6.

    Evaluate by asking:

    • Have I investigated the problem as thoroughly as I could? What problems did I encounter, and how did I overcome them? What would I do differently next time?

    1.

    a. Practical activity.

    b.

    Scatter plot titled 'Transport and Height' measuring the number of boys and height.

    c. No. Both lines rise and fall at the same points, so the two distributions are very similar. The walk and bike line goes higher than the bus and car line only because there are more students in this group.

    2.

    a. 

    Percentage of all walkers and bikers

    Percentage of all bus and car users

    0.8

    2.1

    9.2

    3.2

    19.1

    21.3

    29.9

    36.2

    26.3

    24.5

    11.6

    11.7

    3.2

    1.1


    b.

    Scatter plot titled 'Transport and Height' measuring the percentage of boys in category and height.

    c. Answers will vary but may include these points:

    • There is a very similar percentage of tall boys in both groups.
    • A slightly smaller percentage of the boys who are 170 cm or taller get a ride to school.
    • Of the short boys (those less than 160 cm), a slightly higher percentage is in the group that walks or bikes.
    • The sample is probably too small to prove much.

    3.

    Investigations and results will vary.

    The quality of the images on this page may vary depending on the device you are using.