9.9: Practice and Exploration

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Compute the mean, median, range, and standard deviation of the following five data values: 51, 79, 2, 80, and 38. To compute the standard deviation it is helpful to use a table like the one that is shown in Table 9.6.
Compute the mean, median, range, and standard deviation of the following six data values: 39, 28, 95, 42, 86, and 45. To compute the standard deviation it is helpful to use a table like the one that is shown in Table 9.6.
Compute the mean and the median of the following five data values: 51, 79, 2, 80, and 380. Explain why the mean and median are quite different from another.
Compute the mean and median of the following five data values: 1, 179, 120, 807, and 380. Explain why the mean and median are quite different from another.
Suppose that two exams from two different classes both have means equal to 81. The standard deviation was 15 for the first exam and 7 for the second exam. If a student must score at least 60 to pass the exam, which class would have a larger percentage of students who passed the class? Justify your answer.
Suppose a group of people has the mean age of 25 and the median age of 18 years old. Knowing that the oldest person in the room is 95, which measure of location will provide a better summary of the typical age in the group, the mean or the median?
Suppose that you have taken an exam in a class. The instructor has reported that the mean grade on the exam is 88 with a standard deviation equal to 7. You scored 90 on the exam. Using the empirical rule, decide if your score is unusually high. Explain the logic you used to come to your conclusion.
While having dinner with some friends, someone boasts that their first-year salary after graduating was $150,000. You know that for the alumni from their department the average starting salary is $67,000 with a standard deviation of $8,000. Given this information, how likely is it that this person is being truthful about their starting salary?
You and a friend are both taking the same history class at different times. Suppose in your class, the average is 85 with a standard deviation of 5 on the first exam. For your friend's class, the average is 75 with a standard deviation of 7. You scored a 90 and your friend scored an 89. Using the empirical rule, who did better? Explain.
If you flip a fair coin 100 times, the mean number of times you expect to observe a heads is 50 with a standard deviation of 5. Suppose your friend says they flipped a coin 100 times and got a heads 57 times. Using the empirical rule, state how unusual you think it would be to get heads this many times in 100 flips of a fair coin.
Jessica and Jonathan are planning to go to the same university in the fall. Jessica takes the ACT in January and Jonathan takes it in March. For the math portion of the exam, Jessica scores at the 92nd percentile, and Jonathan scores at the 94th percentile. Who did better on the exam in comparison to the other students who took the same exam?
A family in Illinois gave birth to twins, a boy and a girl. When they are 13 years old, their daughter is in the 82nd percentile for height and their son is in the 73rd. Who is taller for their gender?
Suppose that there are 150 people in a room attending a party and they have written their ages on slips of paper that they have given to the host. The host then computes that their own age is at the 77th percentile for the ages in the group. Approximately how many people at the party are younger than them?
The temperatures over the past year for a small town have been observed, and it is reported that the 25th percentile of the temperatures is 37.5 degrees Fahrenheit and the 75th percentile is 79.2 degrees Fahrenheit. What percentage of the temperatures are between these two numbers? If 365 temperatures have been observed, approximately how many of those will between these two temperatures?

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