Sample Variance and Standard Deviation
3.2 EXERCISES
M03_GROE0383_10_GE_C03.indd 127 23/08/17 4:53 PM
128 Chapter 3
|
Describing Data Using Numerical Measuresa. Compute the range, variance, standard deviation, and interquartile range for these sample data.
b. Briefly explain the difference between the range and the interquartile range as a measure of dispersion.
3-34. Gold’s Gym selected a random sample of ten customers and monitored the number of times each customer used the workout facility in a one-month period. The following data were collected:
10 19 17 19 12 20 20 15 16 13
Gold’s managers are considering a promotion in which they reward frequent users with a small gift. They have decided that they will only give gifts to those customers whose number of visits in a one-month period is 1 standard deviation above the mean. Find the minimum number of visits required to receive a gift.
3-35. A college registrar has been asked to prepare a report about the graduate students. Among other things, she wants to analyze the ages of the students. She has taken a sample of ten graduate students and has found the following ages:
32 22 24 27 27 33 28 23 24 21 a. Compute the range, interquartile range, and
standard deviation for these data.
b. It is thought that the mean age of graduate students in U.S. colleges and universities is 37.8 years.
Based on your calculations in part a, what might you conclude about the age of students in this college’s programs?
3-36. The Government of Malaysia has ended the petrol and diesel subsidies that were introduced in December 1, 2014. The government sets pump prices based on the average cost of refined oil (MOPS fuel) of the preceding month. David is studying the petrol price flows for RON95. He selects petrol prices from the last 10 months (June 1, 2016 to March 1, 2017) for his study. The list of the price (in RM per liter) for RON95 is as follows:
2.3 2.3 2.1 1.9 1.95
1.8 1.7 1.75 1.75 1.7
Source: https://www.imoney.my/articles/latest-petrol- prices-malaysia
a. Compute the variation between the highest and the lowest price per liter for RON95.
b. Compute the standard deviation for the price per liter for RON95.
c. By using the findings in parts a and b, write a short report for David on the dispersion of the price per liter for RON95.
3-37. Alice is the jewelry designer for Diamond & Platinum and she is designing a new diamond collection. Before she starts her design, she is checking on the width of the diamond provided by the company. A sample of 25 diamonds was selected by her and the widths (in mm) for each diamonds were recorded below:
3.98 3.96 4.28 4.42 4.3
3.84 3.98 3.9 4.34 3.92
4.07 4.11 3.84 4.29 3.96
4.23 3.78 4.37 4.26 4.43
4.35 4.05 3.75 4.27 4.47
a. Compute the range, interquartile range, variance, and standard deviation for the diamonds’ width.
b. Assume Alice found that she has wrongly recorded one of the diamonds’ width and replaces 4.47 mm with 4.49 mm. Determine which of the findings in part a is not affected by the change.
c. Suppose the company decides to provide Alice with smaller diamonds and the width of each reduces by 0.1 mm. Would this affect your findings for part a?
3-38. Students in a communications class studied network television programming and found the average nonprogramming minutes in an hour of prime-time broadcasting for network television was 15:48 minutes.
For cable television, the average was 14:55 minutes.
a. Calculate the difference in the average clutter between network and cable television.
b. Suppose the standard deviation in the amount of clutter for both network and cable television was either 5 minutes or 15 seconds. Which standard deviation would lead you to conclude that there was a major difference in the two clutter averages?
Comment.
3-39. Employers typically provide Internet access to assist employees in work-related activities. An IT department officer is monitoring the Internet data usage in a company. She collects the daily amount of data usage (in GB) for a period of 20 days:
45 48 47 46 39
41 35 33 48 44
38 42 44 50 44
40 36 45 49 45
M03_GROE0383_10_GE_C03.indd 128 05/09/17 4:15 PM
3.2 Measures of Variation
|
Chapter 3 129a. Calculate the range, interquartile range, and standard deviation for these data.
b. Which of the finding in part a best represents the variation of daily amount of data usage for the company? Explain.
c. What does the standard deviation indicate about the company’s daily amount of data usage?
3-40. A bus company provides shuttle bus services for a university from 6 a.m. to 8 p.m. Each passenger pays
$1 for a ride. The company decides to adjust the fee based on variations in the numbers of students. If the company found that the variation of the middle 50%
for the number of students who took its service is less than 40 students, then the company will maintain the same fee. If not, it will increase the fee to $1.50. The hourly number of students taking the shuttle service in a day is as follows:
95 108 85 78 80
64 97 99 85 68
65 72 87 98 67
a. Calculate the range and interquartile range for the number of students taking the shuttle service per hour in one day.
b. Based on your findings for part a, if you were to advise the bus company, what do you think should be the final decision that the company should take?
Computer Software Exercises
3-41. The manager of a cell phone store in the Valley Mall recently collected data on a sample of 50 customers who purchased a cell phone and a monthly call plan.
The data she recorded are in the data file called Phone Survey.
a. The manager is interested in describing the
difference between male and female customers with respect to the price of the phone purchased. She wants to compute the mean and standard deviation of the phone purchase price for each group of customers.
b. The manager is also interested in an analysis of the phone purchase price based on whether the use will be for home or business. Again, she wants to compute the mean and standard deviation of the phone purchase price for each group of customers.
3-42. The file MBA Analysis contains data on several variables for eight MBA graduates. The variables include pre– and post–MBA salary, percentage salary increase, undergraduate GPA, average GMAT score, annual tuition, and expected annual student cost.
Compute the mean, median, range, variance, and standard deviation for each of the variables in the database and write a short report that summarizes the data using these measures. Include any appropriate charts or graphs to assist in your report.
3-43. The First City Real Estate Company managing partner asked the office administrator to provide a descriptive analysis of the asking prices of the homes the company currently has listed. This list includes 319 homes; the price data, along with other home characteristics, are included in the data file called First City Real Estate.
These data constitute a population.
a. Compute the mean listing price.
b. Compute the median listing price.
c. Compute the range in listing prices.
d. Compute the standard deviation in listing prices.
e. Write a short report using the statistics computed in parts a–d to describe the prices of the homes currently listed by First City Real Estate.
3-44. Suppose there is an investigation to determine whether the increased availability of generic drugs, Internet drug purchases, and cost controls have reduced out-of- pocket drug expenses. As a part of the investigation, a random sample of 196 privately insured adults with incomes above 200% of the poverty level was taken, and their 2015 out-of-pocket medical expenses for prescription drugs were collected. The data are in the file Drug Expenses.
a. Calculate the mean and median for the sample data.
b. Calculate the range, variance, standard deviation, and interquartile range for the sample data.
c. Construct a box and whisker plot for the sample data.
d. Write a short report that describes out-of-pocket drug expenses for privately insured adults whose incomes are greater than 200% of the poverty level.
3-45. The placement center at a southern university tracks starting salaries. The data file called BI SALARIES lists the starting salaries for the 25 graduates in Information Technology who completed one or more internships prior to graduation.
a. Calculate the mean, median, and standard deviation of the starting salaries for IT graduates.
b. Calculate the 80th percentile for these data.
c. Calculate the third-quartile salary for these data.
3-46. Efficient Hiring, Inc., assists companies in hiring people to fill jobs. The file called Hired contains data on a sample of the placements made by the company.
The two variables in the file are the number of days required to fill the position and the costs incurred (including advertising, interviewing, etc.) to complete the hiring process.
a. Calculate the variance and standard deviation for the sample cost data.
b. Construct a box and whisker plot for the cost data.
Does this plot indicate that extreme values (outliers) may be inflating the measures of spread calculated in part a?
c. Suggest and calculate a measure of spread that is not affected by outliers.
M03_GROE0383_10_GE_C03.indd 129 05/09/17 4:15 PM
130 Chapter 3