135 Homework 6.1 Measures of the Center

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Homework 6.1: Measures of the Center You should complete the homework assignment by due date in Blackboard. Failure to submit the homework by 11:59 PM on the due date will result in a zero on the assignment. Remember that copying another student’s assignment, having someone else complete your assignment, or downloading answers from online are all academic misconduct and will result in a 0 on the assignment. You MAY work together with other students, but you should submit all of your own work. You should show all work on every problem – failure to do so may result in zero credit on the problem. Use this data for problems 1-3. A professor gives an exam to 20 students. They receive the following scores 23 55 65 73 73 76 78 78 81 83 84 85 86 88 88 91 94 96 99 100 1. Find the mean, median, and mode(s) of the data set. 2. A 21 st student takes the exam late and gets a 84. Find the mean, median, and mode(s) of the data set with this student added. 3. What if the 21 st student had not taken the exam and earned a 0? Find the mean, median, and mode(s) of the data set with this student added. Which changed the mean/median/mode(s) more, adding a student with a 82 or with a 0? What do we call a data value like the 0 in this data set? 4. The US government tracks household income – the total amount of money brought in by people living in a single household. In 2014, the median household income was $53, 657. The mean household income was $72,641. Give at least two possible explanations of why the mean would be so much higher than the median. Use this information for problems 5 and 6. A small town consists of a subdivision of 49 houses where every house is worth $50,000 and a single large mansion which is worth $5,000,000. 5. What is the mean home value in the town? What is the median home value in the town? 6. A journalist wants to use the statement, “The average value of a home in the town is _____.” Which number should they use to fill in the blank? Explain why you gave that answer. Use this frequency table for problems 7 and 8. Value Frequency Relative Cumulative Relative

Frequency Frequency 0 23 1 20 2 11 3 23 4 13 5 16 6 14 7. Complete the frequency table with relative and cumulative relative frequencies. 8. Calculate the mean, median, and mode(s). Use the following data for problems 9 and 10. A researcher wants to understand how old children are when they get their first cellphone. They collect the following data: Age Frequency Relative Frequency Cumulative Relative Frequency 11 4 12 13 13 23 14 25 15 13 16 2 9. Complete the table by computing relative and cumulative relative frequency. Use the table to compute the mean, median, and mode(s) of the data set. 10. A journalist wants to use the statements below in an article about cellphone use. What numbers should they use to fill in the blanks? Explain why you gave that answer. a. “Research shows that most children have a cellphone by the time that they are _____.” b. “Research has shown that the most common age for children to get their first cellphone is _____.”

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