5 14.notebook May 14, 2015

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1 Objective: I can represent categorical data using a two way frequency table Entry: A marketing company is trying to determine how much diversity there is in the age of people who drink different soft drinks. They take a sample of people and ask them which soda they prefer. For the two sodas the age of those people who preferred them is given below. A. Which soda appears to have a greater diversity in the age of people who prefer it? How did you decide this? B. Use your calculator to determine the sample standard deviation, normally given as s x, for both data sets. Round your answers to the nearest tenth. Did this answer reinforce your pick from (b)? How? You randomly survey students in your school regarding whether own a cell phone, mp3 player or both. You find that 78 students own a cell phone and of those 57 own a mp3 player. There are 13 students that do not own a cell phone but own an mp3 player. 9 students own neither device. Construct a two way table for this data. Pull A. What percent of students own a cell phone? B. What percent of students own an mps player? C. What percent of students own a cell phone given they have a mp3 player?

2 Brown Eyes Blue Eyes Exercise #1 Let's do a quick categorical survey! By show of hands, how many students fall into each category for eye color? Green Eyes Other Colors Although surveys of data that contain only one category are interesting, statisticians are often interested in how responses to two categories relate to one another. For example: We may want to know how a person s gender (one category) affects what profession (a second category) they would prefer when they grow up. A business might want to know if a persons age (one category) affects the products that they purchase (a second category) This type of data is summarized in a two way frequency table. Exercise #2 A class of 20 students recorded their hair color and eye color which are shown in the two-way frequency table below. Copy table into your n Marginal Relative Frequency the ratio of the sum of the joint relativ frequency in a row or column and the number of data values A How many students had blond hair and blue eyes? Joint Relative Frequency the ratio of the frequency in a particular category and the total number of data values B How many student had Cred hair? Construct a table that shows the joint relative frequencies and the marginal relative frequencies for the data above.

3 Exercise #3 Conditional Relative Frequency the ratio of a joint relative frequency and a related marginal relative frequency. Let s see if there is a connection between eye color and hair color by using conditional relative frequencies. B What is the conditional relative frequency of having green eyes if you have black hair? A What is the conditional relative frequency of having green eyes if you have red hair? (This is equivalent to asking what the percent of people with red hair have green eyes.) C Does it appear that having green eyes has a dependency or at least an association with having red hair? Explain. D Is it more likely that a person with black hair has blue eyes or that a person with blond hair has brown eyes? Use conditional marginal frequencies to support your answer. Exercise #4 A survey of 52 graduating seniors was conducted to determine if there was a connection between the gender of the student and whether they were going on to college. Based on this data, what is more likely: that someone going to college is female or that someone who is female is going to college? These may seem like the same thing, but are quite different.

4 And a worksheet we have. Go forth and worksheet.

5 Objective: I can analyze data with two variables. Assignment: Bivariate Data Anaylsis and Linear Regression WS 1.) Copy/complete the following two way frequency table about male and female volunteers into your notes and answer the following questions. a.) What is the conditional relative frequency of a male volunteering at the hospital? b.) What is the conditional relative frequency of a female volunteering at the animal shelter? c.)what percentage of volunteers are male? Bivariate Data Vocabulary Bivariate data (x,y): correlation Positive Negative Strong Moderate Weak none/ no Causal Relationship Lurking Variable

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7 It's worksheet time!

8 Put on your stats thinking cap and analyze: What do you notice? Did they lie? What if it's true? Is it fair, normal, ou What do you think the answer is? What do you wonder? A sample of the first 100 comments: x = s x = 3.89 IQR = 5 min = 0 Q 1 = 10 med = 15 Q 3 = 15 max = 21

9 Vocabulary Categorical Data Two Way Frequency Tables Categorical Data data that shows how many things surveyed fall into a given category Two Way Frequency Table Joint Relative Frequency the ratio of the frequency in a particular joint relative frequencies category and the total number of data value marginal relative frequencies Marginal Relative Frequency conditional relative frequencies the ratio of the sum of the joint relative frequency in a row or column and the to number of data values Conditional Relative Frequency the ratio of a joint relative frequency and a marginal relative frequency.