standard_description: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
problem_activity: Problem 1
Bobbie is a sixth grader who competes in the 100-meter hurdles. In eight track meets during the season, she recorded the following times (to the nearest one hundredth of a second).
18.11    31.23    17.99    18.25    17.50    35.55    17.44    17.85
a.   What is the mean of Bobbie’s times for these track meets? What does the mean tell you in terms of the context?
b.   What is the median of Bobbie’s times? What does the median tell you in terms of the context?
c.   Explain why the mean is higher than the median.
d.   Which measure of center do you think best represents Bobbie’s 100-meter hurdle time? Explain your reasoning.
e.   The two times that were over 30 seconds were times when Bobbie fell on a hurdle. She decides to take those times out to get a sense of her typical time without falling. What is the new mean? The new median? How do those compare to the original mean and median?
Problem 2
At the University of North Carolina (UNC) in the mid-1980's, the average starting salary for a Geography major was over $100,000 (equivalent to almost $300,000 today).
At that same time, basketball star Michael Jordan was drafted into the NBA with one of the highest salaries in the league. He had just graduated from UNC with a degree in Geography.
a.   Explain why the mean is a misleading measure of center to represent the salary of geography students at UNC.
b.   What measure of center would better represent the salary of geography students at UNC? Explain your reasoning.
Problem 3
The data set below represents the morning commute time of eight colleagues in an office on the same day. The mean of the data set is 32.5 minutes and the median is 38 minutes.
45           32           38           20           5           40           38           42
There was a typo in the data set, and the input “5” was supposed to be “50.” The typo is corrected and the correct mean and median are found.
Without calculating, explain what impact the typo had on the mean and the median.


aligns: no