Statistical Presentation of Data

1. Data collected by the Oil Price Information Service from more than 90,000 gasoline and convenience stores throughout the U.S. showed that the average price for a gallon of unleaded gasoline was $3.28 (MSN Auto website, February 2, 2014). The following data show the price per gallon ($) for a sample of 20 gasoline and convenience stores located in San Francisco.

a.  Use the sample data to estimate the mean price for a gallon of unleaded gasoline in San Francisco (to 2 decimals).

b.  Compute the sample standard deviation (to 4 decimals).

c.  Compare the mean price per gallon for the sample data to the national average price. What conclusions can you draw about the cost living in San Francisco?

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2. The results of a national survey showed that on average, adults sleep 6.9 hours per night. Suppose that the standard deviation is 1.4 hours.  Round your answers to the nearest whole number. 

a. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 4.1 and 9.7 hours. At least  %

b. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 3.9 and 9.9 hours. At least  %

c. Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 4.1 and 9.7 hours per day.  % How does this result compare to the value that you obtained using Chebyshev's theorem in part (a)?

b.  Which of the following scatter diagrams represents the relationship between jobless rate and the percentage of delinquent housing loans.

4. The data contained in the WEBfile named FoodIndustry shows the company/chain name, the average sales per store ($1000s), and the food segment industry for 47 restaurant chains (Quick Service Restaurant Magazine website, August 2013). Click on the webfile logo to reference the data.

a.  What was the mean U.S. sales per store for the 47 restaurant chains? Round your answer to one decimal place.

b.  What are the first and third quartiles?

What is your interpretation of the quartiles?

25% of the restaurants have an average sales per unit  to  and 25% of the restaurant chains have an average sales per store  to  .

c.  Show a box plot for the level of sales and discuss if there are any outliers in terms of sales that would skew the results.

Select the correct box plot:

There is(are)  .

d.  Develop a frequency distribution showing the average sales per store for each segment.

Comment on the results obtained.

The frequency distribution shows that the lowest average sales per store is for the  segment.

First Quartile (to 1 decimal)

Third Quartile (to 3 decimals)

{Exercise 3.23 (Algorithmic)}

7. Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during 2005 and 2006 are as follows:

a. Calculate the mean (0 decimals) and the standard deviation (to 2 decimals) of the golfer's scores, for both years.

b.

c. What is the primary difference in performance between 2005 and 2006?   What improvement, if any, can be seen in the 2006 scores?

8. Five observations taken for two variables follow.

a. Which of the following scatter diagrams accurately represents the data set? 1. 

b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?  

c. Compute the sample covariance.  

d. Compute the sample correlation coefficient (to 3 decimals).   What can you conclude, based on your computation of the sample correlation coefficient?

10. Annual sales, in millions of dollars, for 21 pharmaceutical companies follow.

a. Provide a five-number summary. If needed, round your answer to a whole number.

b.

c. Compute the lower and upper limits. Enter negative amounts with a minus sign.

d.

e. Do the data contain any outliers?  

f. Johnson & Johnson's sales are the largest on the list at $14,138 million. Suppose a data entry error (a transposition) had been made and the sales had been entered as $41,138 million. Would the method of detecting outliers in part (c) identify this problem and allow for correction of the data entry error?  

g. Which of the following box plots accurately displays the data set?

11. Annual sales, in millions of dollars, for 21 pharmaceutical companies follow.

a. Provide a five-number summary.

b.

c. Compute the lower and upper limits.

d.

e. Do the data contain any outliers?  

f. Johnson & Johnson's sales are the largest on the list at $14,138 million. Suppose a data entry error (a transposition) had been made and the sales had been entered as $41,138 million. Would the method of detecting outliers in part (c) identify this problem and allow for correction of the data entry error?  

g. Which of the following box plots accurately displays the data set?

Lower limit

Upper limit

13. Morningstar tracks the total return for a large number of mutual funds. The following table shows the total return and the number of funds for four categories of mutual funds. Excel File:  data03-17.xls  

a.  Using the number of funds as weights, compute the weighted average total return for these mutual funds. (to 2 decimals)  %

b.  Is there any difficulty associated with using the “number of funds” as the weights in computing the weighted average total return in part (a)? Discuss. What else might be used for weights?

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c.  Suppose you invested $10,000 in this group of mutual funds and diversified the investment by placing $2000 in Domestic Equity funds, $4000 in International Equity funds, $3000 in Specialty Stock funds, and $1000 in Hybrid funds. What is the expected return on the portfolio? (to 2 decimals)  %

14. The Wall Street Journal reported that Walmart Stores Inc. is planning to lay off 2,300 employees at its Sam's Club warehouse unit. Approximately half of the layoffs will be hourly employees (The Wall Street Journal, January 25-26, 2014). Suppose the following data represent the percentage of hourly employees laid off for 15 Sam's Club stores.

a.  Compute the mean and median percentage of hourly employees being laid off at these stores.

b.  Compute the first and third quartiles.

c.  Compute the range and interquartile range.

d.  Compute the variance and standard deviation. Round your answers to four decimal places.

e.  Do the data contain any outliers?

f.  Based on the sample data, does it appear that Walmart is meeting its goal for reducing the number of hourly employees?

15. U.S. companies lose $63.2 billion per year from workers with insomnia. Workers lose an average of 7.8 days of productivity per year due to lack of sleep (Wall Street Journal, January 23, 2013). The following data show the number of hours of sleep attained during a recent night for a sample of 20 workers. Click on the webfile logo to reference the data.

a.  What is the mean number of hours of sleep for this sample (to 1 decimal)? 

b.  What is the variance? Standard deviation (to 2 decimals)?