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identify a question to generate appropriate data and predict results
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There are many different ways that potatoes can be prepared for eating.
How would you word a question to find out about people's preferred kinds of prepared potatoes? What results do you predict? Describe a population and a sample that you could use to answer your question.
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distinguish between a total population and a sample
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For what kinds of questions could our class be considered as:
- the total population?
- a sample of a population?
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use a variety of methods to collect and record data
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A Grade 5 class learned that thousands of very large and very small potatoes are left in market gardeners' fields each fall. They decide to investigate only those potatoes that get picked and packaged for sale in grocery stores. What questions might they use to best guide their investigations?
Predict what might be the answer to each question you designed above.
Write out a plan for conducting the investigation. Include information on selecting a sample, collecting the data, recording the data, and displaying the data.
Choose one of the questions you suggested for the Grade 5 class and conduct an investigation according to your plan.
Write about the results of your investigation. What things have you learned about potatoes that get packaged for market?
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create classifications and ranges for grouping data
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Determine what groupings you would use to show changes in students' height throughout the school year (e.g., September to January, January to June).
Determine the age groupings for the most listened-to music. Why did you choose to use the number of intervals you did (e.g., three groups as opposed to four groups)?
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display data by hand or by computer in a variety of ways, including:
- frequency diagrams
- line plots
- broken-line graphs
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Wui-Ching needs to spin a 6, or any of its factors, to win the game he is playing. On a tally chart, record the data from at least 50 spins. Show all your data on
a bar graph. Do you think Wui-Ching is more likely
to win the game or to lose it? Why?
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evaluate the graphic presentation of the data to ensure the clear representation of the results
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A class timed how long it took each person to count to 100 and represented the data in two different ways.
- What is the same about each representation of the data? What is different?
- Do you think one display better reveals the data than does the other? Why?
- Choose another way to present the data. Label your work so others can read your graph quickly and easily.
[Click on image to enlarge.]
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discuss the reasonableness of the data and the results
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Tina, Rex, and Liz are conducting reaction-time experiments with a metre stick. The goal is to catch the metre stick as quickly as possible after it is dropped. Each person has three chances to catch the metre stick. Here are the results.
Explain who has the best reaction time if:
- the lowest number of centimetres on any particular trial wins
- the high and low distance for each person is eliminated
- the average distance for each person is calculated (by adding the three results for each and dividing by 3)
What method do you think is most fair for determining the best reaction time? Explain your reasoning. What number represents the mean reaction distance for all three friends? Make a bar graph to show and verify your calculation.
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make inferences from the data to generate a conclusion
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Four friends each bought a large cold drink on a hot summer day. Explain what each graph tells you about how each person drank.
[Click on image to enlarge.]
Draw a graph to represent how you might drink a cold drink.
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Statistics and Probability (Data Analysis)
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