Discuss the skewness of the data

Assignment Help Applied Statistics

Reference no: EM133052012

Problem Set

Problem 1. Consider an investment of $100,000 that declined to a value of $50,000 at the end of the first year and recovered back to $100,000 at the end of the second year. Calculate the arithmetic mean and the geometric mean of the annual rates of return of this investment, and comment on your results.

Problem 2. There are 7 members of the crew of a space shuttle. On earth they weigh 98, 77, 63, 101, 85, 49 and 94 kilograms. Find the mean, median, population standard deviation and range of the weights on Earth.

Problem 3. The following information shows the calories and fat in 500ml (approx.) drinks available from a number of outlets:

Product	Calories	Fat (g)
Dunkin' Donuts Iced Mocha Swirl latte (whole milk)	240	8
Starbucks Coffee Frappucino blended coffee	260	3.5
Dunkin' Donuts Coolatta(cream)	350	22
Starbucks Iced Coffee Mocho Expresso (whole milk and whipped cream)	350	20
Starbucks Mocha Frappucino blended coffee whipped cream)	420	16
Starbucks Chocolate Brownie Frappucino blended coffee (whipped cream)	510	22
Starbucks Chocolate Frappucino Blended Creme (whipped cream)	530	19

a. For each variable, compute the mean, median, mode, first quartile and third quartile.

b. For each variable, compute the sample variance, sample standard deviation, range, interquartile range, coefficient of variation. Are the data skewed? If so, how?

Problem 4. A bank branch located in a commercial district of a city has developed an improved process for serving customers during the noon-1pm lunch period. The waiting time, in minutes of a sample of 15 customers during this hour is recorded over a week. The results are:

4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.2 4.5 6.1
0.38 5.12 6.46 6.19 3.79

a. Calculate the mean, median, first quartile and third quartile

b. Calculate the variance, sample standard deviation, range, interquartile range, coefficient of variation.

c. Are the data skewed? If so, how?

d. A customer walks into the branch during the lunch hour and asks the branch manager how long a wait she can expect. The branch manager replies, "Almost certainly less than five minutes." On the basis of your results to parts a. -c., comment on the manager's rely.

Problem 5. A population of TSTA602 students is known to have a mean final mark of 65 and a standard deviation of 5. The population is known to be bell-shaped. Describe the distribution of final marks. Is it likely that a student will fail this unit? Is it likely that a student will achieve above 80?

Problem 6.

a. Calculate the 5-number summary for the following data: 5 4 7 13 20 9 12 21 23 19 17
b. Discuss the skewness of the data.

Problem 7. An owner of a restaurant is interested in examining the demand for dessert over a given time period. She is worried that the size of entrées is too large, therefore affecting whether or not patrons order dessert. If this is the case, it would have an impact on her profit. She collects data on whether a dessert is ordered and whether an entrée is ordered for a sample of 1000 patrons. She finds the following:

	Dessert ordered
Entrée ordered	Yes	No	Total
Yes	625	125	750
No	180	70	250
Total	805	195	1000

a. Among the patrons who do not order dessert, what is the percentage of those having ordered entrée? Can the owner make a decision on the size of the entrée based on this percentage? Explain.

b. Produce a side-by-side bar chart and a stacked bar chart based on this contingent table using MS Excel. Comment on these two charts. Discuss again whether the owner should reduce the size of the entrée.

Problem 8. Use the calories and fat data in question 3 (see data in WS3.xlsx), compute

a. The sample covariance

b. The coefficient of correlation

Which do you think is more informative in expressing the relationship between calories and fat? Explain. What conclusion do you reach about the relationship between calories and fat? Produce a scatter plot using MS Excel and comment on the result.

Attachment:- Tutorial Problem Set.rar

Reference no: EM133052012

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