| It is expected that students will:
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formulate a key question from a problem-solving context
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It is Andrea's 13th birthday. She is wondering how many other students in Canada have their 13th birthday today. What questions does she need to ask?
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identify appropriate data sources (first-hand, second-hand, a combination of first and second-hand)
select and justify appropriate methods
of collecting data (designing and using structured questionnaires, experiments, observations, and electronic networks)
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You will often find a relationship between two different body measurements, such as people's head circumference and their height. What are some key questions you might form to guide your investigation of the relationships? Can you predict what conclusion might be expected for each?
Write and carry out a plan for investigating one of your questions. Include information on the following:
- sources of data
- sample size and make-up
- method of data collection
Find two different ways to display your data so that any relationships between body measurements are clearly revealed. Draw conclusions about your investigation, then compare them to your predictions.
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select and justify the choice of an appropriate population sample to use to answer a particular question
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Ray says the taller the basketball player, the more points the player scores. Tell why each of the following examples would or would not provide an appropriate sample to include in Ray's research to verify his prediction. Consider:
- NBA scoring leaders in the last 10 years
- all basketball players on a local high school team
- the centres on last year's provincial teams
- information from a 1990 copy of World Book Encyclopedia
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discuss how the data collected are affected by the nature of the sample,
the method of collection, the sample size, and biases
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Carmen designed and handed out 100 questionnaires
to middle year students in her school. One question
she asked was: "What do you want to be?" Choose one.
| Doctor/Dentist |
Teacher |
| Lawyer |
Sports Manager, Coach or Trainer |
A total of 50 questionnaires were returned. Here are the results.
Carmen concluded that most students will become doctors or dentists. Do you agree with her conclusion? Describe what she might have done differently with:
- the wording of her question
- her method of gathering data
- the sample she chose to survey
- the conclusion she reached
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display data by hand or by computer in a variety of ways, including histograms, double bar graphs, and stem and leaf plots
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The magazine Sports Illustrated for Kids asked many young people this question: "Have you ever played on a sports team where your mom or dad was the coach?"
This table shows the results.
| Yes | | No |
| 42.9% | (dad) | 50% |
| 5.2% | (mom) | |
| 1.9% | (both) | |
Display the survey results on two different types of graphs. Give reasons for your choice of graphs.
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read and interpret graphs that are provided
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Look at this graph showing students' favourite sports.
What are some conclusions you can draw from this graph? Explain your reasoning for each. What important information is not provided by this graph? Could the results be true for the students in your class? Your school? Why?
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describe the general distribution of data:
- smallest and largest value
- frequency (which occurs most often and least often)
- value in the middle
- patterns
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Students in a Grade 6 class measured their heights to the nearest centimetre.
- What are the least and greatest heights? What type of chart or graph would best reveal the two numbers?
- What height occurred more often than any other? What type of chart or graph would best reveal this number?
- What height represents the middle of all the heights? How do you know? What type of chart or graph best reveals this?
| 137 | 115 | 153 | 179 | 164 | 143 | 170 |
| 142 | 129 | 157 | 153 | 128 | 161 | 149 |
| 139 | 164 | 121 | 138 | 161 | 119 | 140 |
| 137 | 157 | 136 | 126 | 149 | 143 | 149 |
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analyse sets of data to make comparisons and test predictions
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Two candidates (A and B) ran for election for school president in 1993. The first graph shows the results. One of the candidates used those results during the 1994 election campaign and prepared the second graph. Can you guess which candidate prepared
the 1994 graph? How did the candidate abuse the information?
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Statistics and Probability (Data Analysis)
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