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129
LEARNING OBJECTIVES
➤ Today I am: examining a survey about school lunches.
➤ So that I can: use frequency tables to compare the data.
➤ I’ll know I have it when I can: decide if there is an association between a lunch
item and being a freshman.
Two-Way
Frequency Tables
LESSON
Exploratory Challenge 1: What’s for Lunch? A total of 247 students were randomly selected to be surveyed about what they liked best for lunch. Melissa and Mike came up with the following statements from the survey. ō Of the 102 freshmen surveyed 18 liked chicken sandwiches and 39 liked salad. ō 85 students total liked pizza. ō Of the 65 students who liked chicken sandwiches, 28 of them were juniors. ō 42 of the 87 sophomores like salad. © bestv/Shutterstock.com © monticello/Shutterstock.com © rvlso!/Shutterstock.com Source: http://www.cpalms.org/Public/PreviewResourceLesson/Preview/
130 Module 1 Descriptive Statistics
- Melissa and Mike would like to present this data to the school administration to get some items placed on the menu permanently, but their data is confusing as written and doesn’t seem to tell the whole story. A. Use the frequency table below to write in what Melissa and Mike know. Pizza Chicken Sandwich Salad Total Freshmen Sophomores Juniors Total B. How many juniors preferred pizza? ____________ C. What was preferred most by freshmen? ____________ D. What was preferred least by sophomores? ____________ E. What is a new question that could be answered using the data table?
- Were the different grade levels of students about equally represented? Why or why not? 45 18 39 102 (^26 1 9 42 ) 14 (^28 16 ) (^85 65 97 ) 14 Pizza Chicken Sandwich No there^ were^ almost (^) twice as many freshmen as (^) Juniors
132 Module 1 Descriptive Statistics
- Collate your class’ data in the frequency table below. Should teachers make social media part of their lessons? Snapchat Instagram Twitter Other Total Yes No Total
- How many students prefer Instagram?
- How many students prefer Instagram AND believe that teachers should NOT make social media part of their lesson?
- What ratio of students prefer Instagram AND believe that teachers should NOT make social media part of their lesson?
- What percentage of students prefer Instagram AND believe that teachers should NOT make social media part of their lesson?
- Use the frequency table to create a column conditional relative frequency table. You’ll need to divide the individual frequencies in each cell by the total at the end of each column. Should teachers make social media part of their lessons? Snapchat Instagram Twitter Other Yes No Total E E 26 6 3 (^3) L 0.5 350 6 2 50 i Iii (^) g I
Unit 1 Measuring Distributions Lesson 10 Two-Way Frequency Tables 133
- Given that a student prefers Snapchat, what is the conditional relative frequency that these students do NOT think teachers should make social media part of their lesson?
- Do you think there is a connection between students who think teachers should use social media and students who like Snapchat best? Explain your thinking.
- You surveyed the members of your school club about the type of end of the year party they would like. Below is a two-way table for the results. A. Complete the table. Males Females Total Miniature Golf 8 4 Skating 3 10 Laser Tag 9 6 Total Using the above data, find the conditional probability of … B. Those wanting laser tag, given that they are female. C. Those wanting miniature golf, given that they are male. D. Females, given that they want laser tag. E. Males, given that they want miniature golf. If a (^) 0.45 45 15 (^20 20 ) 2 f (^8) 0.3 30 0 Zg^ O (^4 ) TE Is 0.4 401 1 82 2 3 0.67 67
Unit 1 Measuring Distributions Lesson 10 Two-Way Frequency Tables 135
- Complete each definition. A. When two sets of numeric data are strongly ________________ together we say they have a ________________ correlation. B. Causation is o!en confused with correlation. Causation is when one event ________________ about another event. C. Association is when there is a ______________________________ between two sets of categorical data. When we see a large difference when comparing two sets of data there is an association. Let’s look at the What’s For Lunch data from the Exploratory Challenge 1 by comparing the column conditional relative frequencies for each choice.
- From the graph we can see that there is a greater percentage of freshmen who want pizza when compared to sophomores or juniors. Therefore there is an association between freshmen and pizza choice. Write two more associations you see in this data. ō ō
136 Module 1 Descriptive Statistics Sometimes it is not clear if there is a causation between two sets of data when you don’t have the data. For each situation below, state if you believe there is a causation or not and the reason why. Situation Causation Statement True or False? Explain.
- Maria states that small dogs are more likely to pass an obedience course. Does a dog’s size cause its ability to pass an obedience course?
- Melissa says that an active social network user is more likely to be a good writer than those people who rarely use a social network.
- Hank believes that there are more men who love country music. Can your gender predict what type of music someone loves?
- Michael says a person from Montana is more likely to choose country music than a person from California?
- Mr. Hill believes that students who don’t do their homework are more likely cut class than those who do their homework. Even if there is a correlation between two events or actions, that does not necessarily mean that one event caused the other to occur.
Unit 1 Measuring Distributions Lesson 10 Two-Way Frequency Tables 139
NAME: PERIOD: DATE:
Homework Problem Set Several students at Rufus King High School were debating whether freshmen or sophomores were more involved in a!er-school activities. There are three organized activities in the a!er-school program— intramural basketball, chess club, and jazz band. Due to budget constraints, a student can only select one of these activities. The students were not able to ask every freshman or sophomore student in the school whether they participated in the a!er-school program or what activity they selected if they were involved.
- Write two questions that could be included in the survey to investigate the question the students are debating.
- Rufus King High School has approximately 1, students. Sam suggested that the first 100 students entering the cafeteria for lunch would provide a random sample to analyze. Janet suggested that they pick 100 students based on a school identification number. Who has a better strategy for selecting a random sample? How do you think 100 students could be randomly selected to complete the survey? © Stoker-13/Shutterstock.com © ingenium/Shutterstock.com © gomolach/Shutterstock.com
Unit 1 Measuring Distributions Lesson 10 Two-Way Frequency Tables 141
- Consider the Rufus King High School data from Problem 3 regarding a!er-school activities. Calculate the row conditional relative frequencies for each of the cells to the nearest thousandth. Place the relative frequencies in the cells of the following table. (The first cell has been completed as an example.) Intramural Basketball Chess Club Jazz Band Total Freshmen =
Sophomores
- Based on your table, what is the relative frequency of sophomores who play basketball?
- If a freshman or sophomore student was selected at random from school, do you think this student would be involved in an a!er-school program? Explain your answer.
- Why might someone question whether or not the students who completed the survey were randomly selected? If the students completing the survey were randomly selected, what do the marginal relative frequencies possibly tell you about the school? Explain your answer.
- Why might freshmen think they are more involved in a!er-school activities than sophomores? Explain your answer.
- For what a!er-school activities do you think the row conditional relative frequencies for freshmen and sophomores are very different? What might explain why freshmen or sophomores select different activities?
142 Module 1 Descriptive Statistics
- If John, a sophomore student at Rufus King High School, completed the a!er-school survey, what would you predict was his response? Explain your answer.
- If Beth, a freshman student at Rufus King High School, completed the a!er-school survey, what would you predict was her response? Explain your answer.
- Notice that 20 freshman students participate in intramural basketball and that 20 sophomore students participate in intramural basketball. Is it accurate to say that freshmen and sophomores are equally involved in intramural basketball? Explain your answer.
- The opinions of 9th grade students in California were compared to the opinions of 9th grade students in Ohio on the same topic of if they’d rather be rich, healthy, happy or famous. Those results are shown in the table below. Rich Healthy Happy Famous Total California 15 15 45 9 84 Ohio 33 6 24 6 69 Total 48 21 69 15 153 Create a row conditional relative frequency table of this data. Rich Healthy Happy Famous Total California Ohio
