Unit Quiz: Statistics

Question 1: Find the mean, median, and mode of the following data set: 12, 15, 18, 15, 22, 15, 28, 19, 15

Question 2: The ages of members in a book club are: 25, 28, 32, 35, 38, 42, 45, 72. Calculate the mean and median. Which measure better represents the typical age? Explain.

Question 3: Calculate the Mean Absolute Deviation (MAD) for this data set: 20, 25, 30, 35, 40

Question 4: Two students tracked their daily step counts for a week.
Student A: 8000, 8500, 7800, 8200, 8100, 8400, 8000
Student B: 6000, 10000, 7500, 9500, 6500, 9000, 8000
Both have approximately the same mean (about 8,143 steps). Which student has more consistent daily activity? Support your answer with calculations.

Question 5: A random sample of 50 students from a school of 800 students found that 30 students prefer pizza for lunch. Estimate how many students in the entire school would prefer pizza. What assumption are you making?

Question 6: Order the data and find Q1, Q2 (median), Q3, and the IQR: 45, 52, 38, 61, 55, 49, 42, 58, 47, 53, 50, 44

Question 7: A basketball player wants to have a scoring average of at least 18 points per game after 10 games. After 9 games, her scores are: 15, 22, 18, 14, 20, 16, 19, 21, 17. What is the minimum number of points she needs to score in game 10?

Question 8: A survey asked 200 randomly selected adults how many hours of sleep they get per night. The results showed a mean of 6.8 hours with a MAD of 1.2 hours. What can you conclude about the sleep patterns of adults in this population?

Question 9: Explain why a researcher surveying customer satisfaction would choose a random sample rather than just asking the first 50 customers who enter a store on Monday morning.

Question 10: The dot plots below show test scores for two classes (imagine the data).
Class A: 70, 72, 75, 78, 80, 80, 82, 85, 88, 90
Class B: 65, 70, 75, 80, 80, 80, 85, 90, 95, 100
Calculate the range for each class. What does comparing the ranges tell you about the performance in each class?

Question 11: A data set has 7 values. The median is 45 and the mean is 48. Six of the values are: 35, 40, 45, 50, 55, 60. What is the seventh value? (Hint: Think about where it must go to keep the median at 45.)

Question 12: A company claims that the average salary of its employees is $65,000. An employee discovers that 45 workers earn $50,000 each and 5 executives earn $200,000 each.
a) Calculate the actual mean salary.
b) Calculate the median salary.
c) Is the company's claim misleading? Explain why or why not.