Year 7 Statistics and Probability Pretest

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Date:

Part 1: Data and Displays

Instructions: Answer all questions. Show working where needed. You may use a calculator only if your teacher allows it.

1. Identify the type of data for each variable. Write categorical, discrete numerical or continuous numerical.

a) Favourite colour: ____________________

b) Number of siblings: ____________________

c) Height in centimetres: ____________________

2. The following information comes from a column graph showing students’ favourite sports.

Football: 8 students Netball: 6 students Basketball: 10 students Tennis: 4 students

a) Which sport was most popular? ____________________

b) How many students were surveyed altogether? ____________________

c) How many more students chose basketball than tennis? ____________________

3. The numbers of books read by seven students in one month were:

2, 5, 3, 5, 7, 4, 2

Calculate the:

a) mean: ____________________

b) median: ____________________

c) mode: ____________________

d) range: ____________________

4. A student says, “The mean number of books is the number that appears most often.” Is the student correct? Explain your answer.

Part 2: Investigations and Probability

5. The daily temperatures, in °C, for one week were:

18, 21, 19, 21, 23, 20, 21

a) Create a dot plot or a stem-and-leaf plot to display the data.

b) What temperature occurred most often? ____________________

6. Two groups recorded the number of minutes they spent reading on one evening.

Group A: 10, 15, 15, 20, 20, 20, 25

Group B: 5, 10, 15, 20, 25, 30, 35

a) Find the median for each group.

Group A: __________ Group B: __________

b) Which group has the greater range? Explain how you know.

7. A school wants to find out whether Year 7 students prefer having sport before or after lunch. Write a suitable statistical investigation plan. Include:

• the question to investigate

• who should be surveyed and how a fair sample could be chosen

• how the results could be displayed

8. A bag contains one red, one blue and one green counter. One counter is chosen without looking.

a) List the sample space.

____________________________________________

b) What is the probability of choosing a blue counter?

____________________

9. A fair six-sided die is rolled once.

a) What is the probability of rolling an even number?

____________________

b) What is the probability of rolling a number greater than 4?

____________________

Teacher Answer Key and Diagnostic Mapping

Answers

1. a) Categorical. b) Discrete numerical. c) Continuous numerical.

2. a) Basketball. b) 28 students. c) 6 students.

3. Ordered data: 2, 2, 3, 4, 5, 5, 7. Sum = 28. Mean = 28 ÷ 7 = 4. Median = 4. Mode = 2 and 5. Range = 7 − 2 = 5.

4. No. The mode is the value that occurs most often. The mean is found by adding all values and dividing by the number of values. For this data, the mean is 4 and the modes are 2 and 5.

5. A correct display has 18 once, 19 once, 20 once, 21 three times and 23 once. The most common temperature is 21°C. A correct stem-and-leaf plot may be:

1 | 8 9

2 | 0 1 1 1 3

Key: 2 | 1 means 21°C.

6. Group A median = 20 minutes. Group B median = 20 minutes. Group A range = 25 − 10 = 15 minutes. Group B range = 35 − 5 = 30 minutes. Group B has the greater range because its data are more spread out.

7. Answers will vary. A strong response includes a clear question, a fair sample such as randomly selecting students from each Year 7 class, and a suitable display such as a column graph or percentage graph. The response should explain how results will be compared.

8. a) {red, blue, green}. b) 1 out of 3, or 1/3.

9. a) Even outcomes are 2, 4 and 6, so the probability is 3/6 = 1/2. b) Outcomes greater than 4 are 5 and 6, so the probability is 2/6 = 1/3.