- Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Complete the table. (2 points)
Data Value (# cars) Frequency Relative Frequency Cumulative Relative Frequency
TOTAL
- To construct the histogram for the data in the table created in question 1, determine the appropriate minimum and maximum x and y values and the scaling. Sketch the histogram by hand, using software like Microsoft Paint, or using Excel. Label the horizontal and vertical axes with words. Include numerical scaling. (1 point)
- Answer the following questions about percentiles. Note: You do not need to do any math to complete these questions. (3 points)
a. For runners in a race, a low time means a faster run. The winners in a race have the shortest running times. Is it more desirable to have a finish time with a high or low percentile when winning a race?
b. The 20th percentile of run times in a particular race is 5.2 minutes. Write a sentence interpreting the 20th percentile in the context of the situation.
c. A bicyclist in the 90th percentile of a bicycle race completed the race in 1 hour and 12 minutes. Is he among the fastest or slowest cyclists in the race? Write a sentence interpreting the 90th percentile in the context of the situation.
- On an exam, would it be more desirable to earn a grade with a high or low percentile? Explain. (1 point)
- Use the following information to answer the next three exercises: The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest: 16, 17, 19, 20, 20, 21, 23, 24, 25, 25, 25, 26, 26, 27, 27, 27, 28, 29, 30, 32, 33, 33, 34, 35, 37, 39, 40. (3 points)
a. Calculate the mean.
b. Identify the median.
c. Identify the mode.
- When the data are skewed left, what is the typical relationship between the mean and median? (1 point)
- When the data are symmetrical, what is the typical relationship between the mean and median? ( 1 point)
- Describe the shape of this distribution. (1 point)
- Describe the relationship between the mode and the median of this distribution. (1 point)
- Are the mean and median the exact same in this distribution? Why or why not? (1 point)
- Answer the following questions about the box plot below. (5 points)
a. Which quarter has the smallest spread of data? What is that spread?
b. Which quarter has the largest spread of data? What is that spread?
c. Find the IQR.
d. Are there more data in the interval 5-10 or in the interval 10-13? How do you know this?
e. Which interval (on the scale of observations 0-13) has the fewest data in it? How do you know this?
i. 0-2
ii. 2-4
iii. 10-12
iv. 12-13
v. need more information
- John tracks the amount of money he spends on fitness each year, including classes, equipment, and clothing purchases. Calculate the mean, median, standard deviation, the first quartile, the third quartile, and the IQR. (6 points)
Year 2005-06 2006-07 2007-08 2008-09 2009-10 2010-11
$ Fitness 1,585 1,690 1,735 1,935 2,021 1,890
Sample Solution