LESSON 1: WHAT IS BIVARIATE DATA?

Transcription

1 LESSON 1: WHAT IS BIVARIATE DATA? Review our Unit Assessment from the previous unit. Write our wonderings about bivariate data. Write a goal stating what ou plan to accomplish in this unit. Based on our previous work, write three things ou will do differentl during this unit to increase our success. Copright 015 Pearson Education, Inc.

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3 LESSON : ARM SPAN AND HEIGHT Erin measured the height and arm span of of her friends. She recorded these data in a chart. Name Height (in.) Arm Span (in.) Abb Blake 5 53 Carlos 0 59 Donna 5 5 Emma 7 75 Franz Gabb 5 Heimlich 5 5 Inez 9 Josh Which of these scatter plots best represents the data that Erin found? A Arm Span (in.) B Arm Span (in.) Height (in.) Height (in.) C 90 D Arm Span (in.) Arm Span (in.) Height (in.) Height (in.) Copright 015 Pearson Education, Inc. 5

4 LESSON : ARM SPAN AND HEIGHT. On a graph like the previous ones (with height on the -ais and arm span on the -ais), what would a point that is close to the -ais but far awa from the origin represent? A A tall person with ver short arms B A short person with ver long arms C A person with equal arm span and height D A tall person with ver long arms 3. How could Erin get a more diverse sample of data on height versus arm span? A Measure the same people again B Measure ever eighth grade student in the school C Measure a random sample from students in all grades K 1 in the whole cit D Measure her three famil members at home. Which of these scatter plots could be modeled b a linear function? A B C D 5. A new scatter plot shows a positive association for hand length (-ais) versus hand span (-ais). What would an outlier close to the -ais, but with a high -value, indicate? Challenge Problem. Collect data on the arm span and height of a few of our famil members or friends. Organize the data on a graph. Do ou notice an correlation? Eplain our results. Copright 015 Pearson Education, Inc.

5 TV Time (hr) TV Time (hr) TV Time (hr) Grade Unit : Bivariate Data LESSON 3: COLLECTING DATA 1. Marshall thinks that the data on hours spent watching TV and hours spent plaing video games will be related. He thinks that people who pla a lot of video games probabl don t watch much TV. If Marshall is right, these data would show a negative association (a person who plas a lot video games will spend less time watching TV). Which graph best represents Marshall s theor? A B Video Game Time (hr) Video Game Time (hr) C D TV Time (hr) Video Game Time (hr) Video Game Time (hr) Copright 015 Pearson Education, Inc. 7

6 LESSON 3: COLLECTING DATA. Jacob collected data on hours plaing video games and hours watching television. He figured people who watch a lot of TV will also pla a lot of video games. He recorded his data as a scatter plot. Do the data show a negative or positive association? 1 1 TV Time (hr) Video Game Time (hr) 3. What does the point wa off to the right represent? A Someone who doesn t watch TV or pla an video games B Someone who plas lots of video games but doesn t watch an TV C Someone who watches lots of TV but doesn t pla an video games D Someone who watches and plas an equal amount of TV and video games Copright 015 Pearson Education, Inc.

7 LESSON 3: COLLECTING DATA. Pedra collected data on students age and forearm length, thinking that the older students would have longer forearms. She organized her data as a scatter plot. Forearm Length (in.) Age (mo) What tpe of association is shown in this scatter plot? A Positive association B Negative association C No clear association D Clear linear association 5. The average -ear-old bo is 3 in. tall. If the average 3-ear-old is 37 in. tall, and the average -ear-old is 0 in. tall, how tall would the average 0-ear-old be? Does our answer make sense? Wh or wh not? Challenge Problem. Determine another set of traits about people that ou think would have a strong positive association. Collect data on our famil or friends to see if our idea is supported b our findings. Copright 015 Pearson Education, Inc. 9

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9 LESSON : GRAPHING DATA 1. Which scatter plots would show a strong positive association? There ma be more than one correct answer. A Height vs. head circumference B Hand width vs. hand span C Cost vs. the quantit of an item purchased D Foot length vs. neck circumference. How would ou describe the association shown in this scatter plot? In the graph above, if there were a point with an -value of 0 what do ou think its -value would most likel be? A B C D Cannot be determined. Which points are likel to be from a scatter plot with a strong positive association? A (, ), (, 5), (, 9), (, 1) B (, 7), (5, ), (, 5), (, ) C (5, 7), (, 7), (13, 7), (15, 7) D (1, 1), (3, ), (, ), (, 1) Copright 015 Pearson Education, Inc.

10 LESSON : GRAPHING DATA 5. Marshall collected data on hours spent plaing video games and the results from a ruler drop test. In a ruler drop test, a person attempts to catch a falling ruler as quickl as possible. Lower values for the ruler drop indicate faster reaction times, since the mean that the ruler fell less distance before being caught. His thoughts were that people who pla lots of video games would have faster reaction times. Here are the data he collected. Inch Mark on Ruler Drop Video Game Time (hr) Was Marshall s idea right? Eplain wh the data support or do not support his claim. Challenge Problem. Graph the following points and eplain an correlation ou see from the graph Copright 015 Pearson Education, Inc. 11

11 LESSON 5: ARM SPAN VSF HEIGHT 1. Which line indicates that an change in will result in the same change in? A B C D How would an outlier affect the placement of the line that best describes the data in a scatter plot? 3. The equation for the line on a scatter plot is = If the value of the independent variable is 1, what is the value of the other variable? A 1 B 13 C 1 D 15 Copright 015 Pearson Education, Inc. 1

12 LESSON 5: ARM SPAN VSF HEIGHT. What does a slope of 0 for the line of a scatter plot indicate? Can ou think of a situation where this slope could occur? 5. Draw a line of best fit for this scatter plot. What is the equation of the line? 5 Challenge Problem. A scatter plot has a strong nonlinear association. Would a line be the best representation of the data? Wh or wh not? Copright 015 Pearson Education, Inc. 13

13 LESSON : WHAT S MY LINE? 1. Where do ou think a line should be placed to best describe the data, knowing that the line will pass through the origin? Wh should the line be placed there? Pedra drew this line to describe the data: What is the slope of the line? A 1 B 1 C 1 D. What is the location of the -intercept? A (, 0) B (1, 1) C (0, 0) D (0, ) 5. What is the equation of the line? Copright 015 Pearson Education, Inc. 1

14 LESSON : WHAT S MY LINE? Challenge Problem. Draw a scatter plot where the line that best represents the data does not pass through an points. Copright 015 Pearson Education, Inc. 15

15 LESSON 7: CHOOSING AN INVESTIGATION The owner of an ice cream truck records the amount of sales each da during the summer, and also keeps track of how hot it was outside each da. This table shows the data he collected. Temperature ( C) Sales ($) Without creating a scatter plot, how do ou think these data will be associated? A Hotter das will have clearl lower sales. B Hotter das will have clearl higher sales. C There is no correlation between temperature and sales. D There will be a weak correlation, with man outliers.. The owner thinks that hotter das will be associated with more sales. Which scatter plot best shows this hpothesis? A B Sales Sales Temperature Temperature C D Sales Sales Temperature Temperature Copright 015 Pearson Education, Inc. 1

16 LESSON 7: CHOOSING AN INVESTIGATION 3. Using the data table from problem 1, create the scatter plot of the data the ice cream truck owner collected. 1,00 1,000 Sales ($) Temperature ( C). What tpe of association is shown from our scatter plot? 5. Was the owner right? Eplain how the real data justif or do not justif his hpothesis. Challenge Problem. Describe another scenario where an eternal force would dramaticall change the sales of a product. Describe the correlation that ou think would eist, and eplain how ou would collect data to support our claim. Copright 015 Pearson Education, Inc. 17

17 LESSON : BIVARIATE INVESTIGATION 1. Scientists recentl discovered a new species of bird that lives b swamps and wades in the water, eating small things at the bottom of the swamp. The recorded the following statistics. Bird Sample Leg Length (in.) Beak Length (in.) A 1 17 B 15 C 1 19 D E 1 F 15 0 G H 1 1 I J 13 1 K 11 1 L 1 1 Do ou think there is a relationship between leg length and beak length? Wh or wh not?. Graph the data from the table and place a line in the location that ou think best represents the data. Eplain wh ou placed the line where ou did Beak Length (in.) Leg Length (in.) Copright 015 Pearson Education, Inc. 1

18 LESSON : BIVARIATE INVESTIGATION Marshall graphed the data and drew a line to represent the data Beak Length (in.) Leg Length (in.) 3. What is the slope and -intercept for the line? A Slope 1; -intercept 0 B Slope 5; -intercept 0 C Slope 1; -intercept 5 D Slope 5; -intercept 5. What is the equation of the line? A = 5 B = + 5 C 1 = D = 5 5. Describe the relationship between leg length and beak length. Challenge Problem. If a bird of the same species were measured and found to have a beak in. long, what would be a good estimate of the leg length? Wh? Copright 015 Pearson Education, Inc. 19

19 LESSON 9: TWO-WAY TABLES 1. How man people participated in the surve shown? Do ou get good grades? Yes No Do ou pla sports? Yes 0 No A 0 people C 30 people B people D 0 people. What percent of students who pla sports also get good grades, according to the table in problem 1? A 50% B 71% C 77% D 5% 3. Which of these statements are supported b the table? There ma be more than one correct statement. Height 5 in. > 5 in. Bos 3 11 Girls 1 A Most bos are taller than 5 in. B Most of the students that are 5 in. tall or less are girls. C Most girls are 5 in. tall or less. D Most of the students that are taller than 5 in. are bos. Copright 015 Pearson Education, Inc. 0

20 LESSON 9: TWO-WAY TABLES. What does the table show? How do ou get to school? Bike Car Bus Walk Do ou eat breakfast regularl? Yes 1 No How is the Venn diagram like a two-wa table? Do ou do chores? Do ou get an allowance? 17 3 Challenge Problem. Talisha asked 0 classmates if the wear shoes or sandals, and if the like the beach or not. Create a two-wa table based on the following surve results: 0 of the 0 students said the liked the beach. Of those 0, 30 students wear shoes regularl as well. 55 of the 0 students said the wore sandals. Of those 55 onl 5 said the don t like the beach. Use this blank table as a guide. Likes Beach Doesn t Like Beach Shoes Sandals Copright 015 Pearson Education, Inc. 1

21 LESSON : CREATING TWO-WAY TABLES 1. Fill in the missing values of this two-wa table. This table represents data for 50 students in total. Plas a Sport Doesn t Pla Sports Total Takes a Language Class Doesn t Take a Language Class Total 50. A two-wa table shows that 75% of students who are in the band also are on the track team. However, onl % of the students surveed were both in the band and on the track team. What might the table look like? 3. Talisha surveed 0 students at her school. She found that of the 0 students of them own a smart phone; 5 of those students also own an MP3 plaer. There are students who don t have a phone but do have an MP3 plaer. There are students who don t have either device. Create a two-wa table to show this information, using the blank table as a guide. MP3 Plaer No MP3 plaer Total Smart Phone No Smart Phone Total 0. There were 0 customers in a restaurant who were asked whether the liked chicken or beef and whether the liked rice or pasta. Out of 30 customers that liked rice 0 liked chicken. There were 0 customers that liked chicken. Use this information to construct a two-wa table. 5. As a group of 5 people entered a movie theater, Erin counted how man of the people had popcorn and how man had a drink. She found that out of people who had popcorn onl people did not have a drink. Si people walked in without popcorn or a drink. Use this information to construct a two-wa table. Copright 015 Pearson Education, Inc.

22 LESSON : CREATING TWO-WAY TABLES Challenge Problem. Take a surve (of our friends and/or famil) of two characteristics that ou believe will show a strong association. Put our data into a two-wa table and eplain whether or not our data supported our idea. Copright 015 Pearson Education, Inc. 3

23 LESSON 11: PUTTING IT TOGETHER Read through our Self Check and think about our work in this lesson. Write down what ou have learned during the lesson. What would ou do differentl if ou were starting the Self Check task now? Which method would ou prefer to use if ou were doing the task again? Wh? Compare the new approaches ou learned about with our original method. Record our ideas keep track of problem-solving strategies. Complete an eercises from this unit ou have not finished. Copright 015 Pearson Education, Inc.

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