Statistics & Probability

Transcription

1 Name: Homeroom: Statistics & Probability Student Learning Expectations Outcome I can collect, display and analyze data to solve problems by: Checking for Understanding creating, labeling and interpreting line graphs to draw conclusions. selecting, justifying and using appropriate methods to collecting data, including: Questionnaires Experiments Databases Electronic media graphing collected data, and analyzing the graph to solve problems. creating, labelling and interpreting line graphs to draw conclusions. Outcome I can use experimental or theoretical probabilities to represent and solve problems involving uncertainty by: demonstrating understanding of theoretical and experimental probability

2 Introduction to Data Analysis 1. Read each of the following statements. Write down a question that could have resulted in each response. a) Most families in Canada own two or more T.V. sets. b) The average grade 6 student spends 1.5 hours per day surfing the internet. c) The most popular movie in the summer of 2007 was Spiderman Tell if each of the following is first hand data or second hand data. a) A photograph of the Acropolis b) A math textbook c) Walking along the Great Wall of China d) An autobiography e) Reading information off the internet f) Interviewing someone for a report 3. Which type of data is more reliable? Why? ~ 2 ~

3 Sampling 1. Leah designed the following questionnaire. She handed it out to the students in her Middle School. Leah reached the conclusion that most students will become doctors or dentists. Tell if you agree with each, and describe what else she might have done: a) the wording of Leah s question b) the method of gathering data c) the sample she chose to survey d) the conclusion she reached. e) the was no bias in this questionnaire. ~ 3 ~

4 2. Tell which is the better sample for each question. a) How many people own a pet? - people shopping at the mall - people shopping at Petland - 5 people walking down the street b) How many people enjoy watching football on T.V? - people shopping at the mall - people shopping at Sport Check - students in a Kindergarten class 3. Identify the bias in each of the following statements. Re-write each question to eliminate the bias. a) Grade 1 students were asked who is their favourite hockey team. b) Fred went to the Mr. Lube and asked how many people owned a car. c) Kaylee asked 50 students if they enjoy going swimming on weekdays. ~ 4 ~

5 I can select, justify and use appropriate methods to collect data including: questionnaires, Experiments, databases, electronic media. 1. Design a questionnaire for collecting data to answer each question. a) Which spread to put on toast is most preferred by your friends? b) What is the favourite weekend activity of students in your class? c) Which Canadian city would the students in your class most like to visit? 2. Cole and Sharlene experimented by playing the game Rock, Paper, Scissors. They wanted to answer this question: Which action wins most often? Here are the data the students collected. Action Number of Wins Rock 9 Paper 11 Scissors 10 Use these data. What conclusions can you make? Explain. 4. Which method would you use to collect data to answer this question: How many times can you clap your hands in 20 s? Explain your choice of method. Collect the data. Answer the question. ~ 5 ~

6 Scatter Plots and Line Graphs 1. Make a scatter plot (series of points graph) for the data. Age Height b) Describe the trend of the graph.

7 3. Why is there a straight line between ? 4. Describe the trend of the graph. 5. What do you notice about the trend of the graph? 6. As grip strength increases, what happens to the arm strength? ~ 7 ~

8 Bar Graphs Patrons at the Mall Number of People Days of the Week 1. What trend do you notice about the number of patrons who visited the mall? 2. Why do you suppose there was a decline in the number of people who went to the mall on Wednesday? 3. How many more people visited the mall on Friday, compared to Tuesday? 4. How many people went to the mall from Monday to Friday? 5. Create a line graph to display the same results. ~ 8 ~

9 6. What conclusions can you make about the data? 7. Why do you think attendance in school and Science grades are related? 8. Billy s attendance was 60%, estimate his Science grade and explain your estimate. 9. Whose attendance percentage was the lowest? 10. How does attendance affect Science grades? 11. Create a line graph to display the same results. ~ 9 ~

10 I can graph collected data, and analyze the graph to solve problems. You will need grid paper. 1. Louisa surveyed the Grade 6 students in her class to answer this question: What is your favourite type of dance? The table shows the data she collected. Type of Dance Number of boys Number of girls Break dancing 3 2 Hip hop 4 3 Texas line dancing 3 5 Ballet 1 3 Other 4 2 a) Draw a graph to display these data. Explain your choice of graph. b) Which type of dance is most popular? Explain. ~ 10 ~

11 Line Graphs 1. Which year was Sarah s car worth the most? 2. Describe the trend of the line graph. Temperatures In NY City Day Temperature 1 43 F 2 53 F 3 50 F 4 57 F 5 59 F 6 67 F 3. Create a line graph to display the results. Write 3 statements to describe the trend of the graph. ~ 11 ~

12 I can create, label and interpret line graphs to draw conclusions. 1. Would you use a line graph or a series of points to display each set of data? Explain your choices. a) the volume of milk in a glass as it is filled b) the number of games won by the Vancouver Canucks each month in the regular season c) the distance travelled by a mail carrier as she covers her route 2. What does this line graph show? a) About how much did the baby elephant weigh at each age? i) birth ii) 1 month iii) 6 months iv) 1 year b) During which month did the elephant gain the most mass? The least mass? How does the graph show this? You will need grid paper. ~ 12 ~

13 1. One afternoon, Angela measured the temperature outside her house every hour. Time (P.M.) 1:00 2:00 3:00 4:0 0 Temperature ( C) 5:00 6: a) Draw a line graph to display these data. b) How did you choose the scale on the vertical axis? c) What conclusions can you make from the graph? ~ 13 ~

14 2. This table shows the number of people living in Red Deer, Alberta from 2002 to Year Populatio n a) Draw a graph to display these data. (Write each population to the nearest thousand.) b) Did you join the points? Explain. c) What do you know from looking at the graph? ~ 14 ~

15 Introduction to Probability 1. Use the following terms to describe the probability of each event: Never less likely equally likely more likely always a) You will have a birthday this year. b) All insects fly. c) Tomorrow will be Friday. d) If you toss a coin twice, it will land tails. e) It will snow someday this week. f) You will have a sandwich this week for lunch. g) You will write the letter e sometime today. h) Tree talk to each other when no one is around. i) There is a rain forest in the Yukon. j) You will one day become a famous movie star. Outcomes 1. Explain what all of the possible outcomes could be in each situation. a) Tossing 2 coins in the air b) Possibility of having a test today c) Rolling a sum of 7 on two 6-sided die d) Pulling out a 4 or a 2 from a deck of cards 2. Write the probability of each situation as a fraction. a) A coin landing heads b) Rolling a 6 on a 6-sided die c) Pulling a 5 of hearts d) Pulling out a red card from a deck of cards from a deck of cards ~ 15 ~

16 Theoretical Probability 1. If a 6-sided die is thrown, what is the probability of each of these events occurring? a) The number showing is a 3? b) The number showing is less than 5? c) The number showing is a composite number? d) The number showing is a 6? e) The number showing is prime? f) The number showing is an odd number? g) The number showing is 3 or less? h) The number showing is a multiple of 2? 2. Write a statement about an event, rolling a 6-sided die to match each of these probabilities. 3 a) The probability of spinner a 4 is b) The probability of spinner a 6 is ~ 16 ~

17 Experimental Probability Each chart shows the results of a probability experiment. Complete the questions for each chart. Coin Toss 1. What is the theoretical probability of landing heads? Heads Tails 2. What is the theoretical probability of landing tails? How many times was the coin tossed? 4. What is the experimental probability of the coin landing heads? 5. What is the experimental probability of the coin landing tails? 6. How do the experimental probability and theoretical probability compare? Paper Cup Toss On the side On the top On the bottom How many times was the cup tossed? 1. What is the theoretical probability of landing on the top? 2. What is the theoretical probability of landing on the bottom? 3. What is the theoretical probability of landing on the side? 5. What is the experimental probability of the cup landing on the top? 6. What is the experimental probability of the cup landing on the side? 7. What is the experimental probability of the cup landing on the bottom? 8. How do the experimental probability and theoretical probability compare? ~ 17 ~

18 Ashley has 15 socks in her drawer. 5 of her socks are white, 6 of her socks are black and 4 of her socks are blue. a) What is the theoretical probability that Ashley will pull out a white sock? b) What is the theoretical probability that Ashley will pull out a black sock? c) What is the theoretical probability that Ashley will pull out a blue sock? d) If Ashley repeated her experiment 60 times, how many times would the sock be: i. White? ii. Black? iii. Blue? e) If Ashley repeated her experiment 150 times, how many times would the sock be: i. White? ii. Black? iii. Blue? ~ 18 ~

19 I can demonstrate an understanding of probability. 1. Anya rolls an octahedron labelled A, A, A, B, C, C, C, C. What is the theoretical probability that the octahedron will land on each letter? 2. Eva s penny jar contains 25 pennies from 2004, 32 pennies from 2006, 17 pennies from 2007, and 26 pennies from She picks a penny from the jar at random. a) List the possible outcomes. b) What is the theoretical probability of each outcome? i) Eva picks a penny from ii) Eva picks a penny from an even-numbered year. iii) Eva picks a penny from a leap year. 3. Yannick is playing a game at a fun fair. Twenty-five small metal boats are floating in a large tub. On the bottom, 20 boats are marked Too bad, 4 boats are marked Take another turn, and 1 boat is marked You win! Yannick uses a magnet on a stick to pull a boat from the tub. What is the theoretical probability of each outcome? a) Yannick loses on his first turn. b) Yannick gets a second turn. c) Yannick wins on his first turn. d) Yannick gets a second turn. e)yannick wins on his first turn. Probabilities compare with the theoretical probabilities? Explain. ~ 19 ~

20 Show What You Know 1. Suppose you want to find out about your classmates favourite sports team. a) Design a questionnaire. b) Ask the question. Record the results. c) What did you find out? 2. Predict how many times you can write the word experiment in one minute. Work with a partner and take turns writing the word and timing one minute. Record your results. Compare your results with your prediction. What conclusions can you make? ~ 20 ~

21 3. For each question below, choose an appropriate method to collect data to answer the question. Explain your choices. (Experiment, Questionnaire, Database) a) What are the 5 largest countries by area in the world? b) What is the favourite summer activity of students in your class? c) How many steps does it take a Grade 6 student in your school to walk from one end of the hallway to the other? 4. Would you use a line graph or a series of points to display wach set of data? Explain a) the number of DVDs sold by a store every day for 1 week. b) the volume of water in a swimming pool as it fills c) the temperature of an oven as it heats up d) the poplulation of Whitehorse from Trevor used the Statisitcs Canada Website to find the number of Canadians who visited various destinations in The table shows the data he coolected. Draw a graph to display these data and what conclusions can you make from the graph? ~ 21 ~

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23 6. Find the theoretical probability of each outcomes. Order the outcomes from most likely to least likely. a) the pointer on this spinner lands on red. RED GREEN b) tossing a coin and getting heads c) rolling a die labelled 1 to 6 and getting 5 BLUE d) randomly picking a red marble from a bag that contains 3 green, 5 blue and 1 red marble. 7. Nalren and Chris made up a game with a spinner. It has 8 equal sectors labelled: 6, 24, 9, 29, 15, 7, 18, 12. Nalren wins if the pointer lands on a multiple of 2. Chris wins if the pointer lands on a multiple of 3. a) Is the game fair? b) What is the theotretical probability that the pointer will land on a multiple of 3? c) Make the spinner. Play the game 20 times and record the results. What is the experimental probability of landing on a multiple of 3? How do these probabilities compare? ~ 23 ~