Data Management

Performance Stations in Math
Data Management
Grade 9
by
Liliane Gauthier
Teacher / Educational Consultant
Saskatoon Board of Education

2. Data Management
Grade 9
D-9, D-17

Materials:
calculator

The following are student marks for a final math exam.

79 26 67 89 99
67 69 80 56 79
96 91 67 79 45
90 89 75 84 59
89 75 56 52 77
74 69 71 60 67

Organize the data in a stem-and-leaf plot.

Calculate the mean, median and mode.

Prepare a box-and-whiskers graph. You will need to find the extremes, and the first and third quartiles.

Analyse the data and write a few sentences about your box-and-whiskers graph.

6. Data Management
Grade 9
D-15, D-16, D-17

Materials:
calculator

1.	Give a set of 10 different numbers with a mean of 12.
2.	List 6 numbers where the mean is greater than the median.
3.	What two values could be added to the set if numbers below so that the mode is 15? 5 8 8 15 20 25
4.	The mean of the results of a quiz is 5. The median is also 5 and the mode is 6. The extremes of the 13 marks are 2 and 10.
	a)	List the marks that could produce these results.
	b)	If a mark of 15 was added to the list, how would each of the following change?
		i.	the mean?
		ii.	the median?
		iii.	the mode?
		iv.	the extremes?
5.	Explain why each of the following people might select the mean, median or mode in a set of data.
	a)	A store owner deciding on what size shoes to order.
	b)	Someone moving to a new city and looking at housing costs.
	c)	Reporting the average score on a test.

11. Data Management
Grade 9
D-25, D-26

Materials:
  spinner (four 90 degree sections) or
  4-sided dice or
  bag with 4 different cards

A breakfast cereal company has randomly placed one of four prizes in each cereal box it manufactures. Consumers are challenged to collect all four in the collection.

Use a Monte Carlo simulation to determine how many boxes need top be purchased in order to be sure you will collect at least one of each prize. Copy and complete the chart below to document the number of spins/throws/picks required to get at least one of each 1, 2, 3, or 4, which represent each prize.

Trial	Prize 1	Prize 2	Prize 3	Prize 4	Total Spins/Throws/Picks
1
2
3
4
5
...

Explain how you would use the different trials to determine your answer.

How could companies change the odds in a country as large as Canada?

12. Data Management
Probability: Grade 9
D-26, D-29

Materials:
toothpicks
chart paper

1.	Draw vertical lines on large chart paper exactly 2 toothpick lengths apart.
2.	Toss 100 toothpicks randomly on the chart paper.
3.	Record any toothpick that touches a line as a "hit".
4.	Calculate the ratio of the number of tosses and the number of hits. Record.
5.	Repeat two more times. Record. Compare results.
6.	What variables could you change in this investigation to further compare results?
7.	Test your ideas and record.

13. Data Management
Probability: Grade 9
D-26, D-29

Materials:

Farmers need information about their crops. They need to know the amount of insecticides and herbicides to use as well as what kind they must use.
1.	How do farmers and scientists predict the the number and species of insect pests in their crops?
2.	How do farmers and scientists predict the the number and variety of weeds in their crops?
3.	How is this information used by the Department of Agriculture?

15. Data Management
Probability: Grade 9
D-30, D-31

Materials:
spinner with four equal sections
spinner with five equal sections

nbsp A number spun on on Spinner A is multiplied a number spun on Spinner B.
1.	Experiment to see if you can determine the probability of the product being 5 or less. Draw a diagram or table to explain your reasoning.
2.	Experiment to see if you can determine the probability of the product being even. Draw a diagram or table to explain your reasoning.
3.	Experiment to see if you can determine the probability of the product being a multiple of 5. Draw a diagram or table to explain your reasoning.
4.	Can how you can calculate the probabilities described above without spinning the counters.
5.	What is the probability of the product being 1?

16. Data Management
Probability: Grade 9
D-26, D-29

Materials:
three pennies

You toss three pennies.
1.	What is the probability that they will all land heads?
2.	What other events are possible?
3.	Are all events equally likely? Explain.
4.	What is the probability of getting two heads and one tail?
5.	Justify your answer b using pennies to illustrate all possible outcomes.

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