Frequency Distribution and Sampling NB-

Frequency Distribution and Sampling

NB- click inside the excel object to see calculations

Use the link below to explore how to plot normal distribution in a spreadsheet and how to find the cumulative probability.

http://www.vertex42.com/ExcelArticles/mc/NormalDistribution-Excel.html

To get the best deal on a CD player, Tom called eight appliance stores and asked the cost of a specific model. The prices he was quoted are listed below: Find the Standard deviation

It was determined that 8.18% of CD cost lie below the minimum value (115), 3.92% lie above the maximum cost (411) and 87.90% lie between 125 and 411.

When investigating times required for drive-through service, the following results (in seconds) were obtained. Find the range, variance, and standard deviation for each of the two samples, and then compare the two sets of results.

Notice that the variance and standard deviation were calculated using excel's formula. There is less variation within drive through times for restaurant A than restaurant B, according to the results above. However, conducting a t-test suggests that, there is no significant difference (p=0.72 > ?=0.05) between the means of their respective drive through times.

3. A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the standard deviation. Find the standard deviation of the data summarized in the given frequency distribution.

It was determined that 6.14% of employee salary lie below the minimum value, 8.94% lie above the maximum cost and 84.92% lie between minimum and maximum salary.

4. The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency distribution below summarizes the results. Find the standard deviation.

5. The heights of a group of professional basketball players are summarized in the frequency distribution below. Find the standard deviation.

PART II

1. Stratified sampling -- students were selected by allocating a proportion of approximately 10% to each class (strata).

2. Simple random sampling -- each contestant was selected by chance and each of them have an equally-likely chance of being selected among the three sample.

3. Yes, No (i.e. this is a random sample but NOT simple random sample), because all teachers in the selected schools have an equally-likely chance of being interviewed, and the selected sample does not represent teachers from other schools in the district that were not included in the selection. Instead, this is cluster sampling

4. Yes. No. It is systematic sampling but with people randomly selected based on each 20th person from the voters' list.

5. No. No. (i.e. this is neither a random sample nor simple random sample), because the females who attended the meeting were not selected and not all females in the company had an equal chance of talking to the personnel manager.

Reference

1. George W. Snedecor, & Cochran, William G. (1989). Statistical Methods (8th ed.): Blackwell Publishing Professional.

2. William G. Zikmund, & Babin, Barry J. (2007). Exploring Market Research 9th.

3. Graham Upton, & Cook, Ian (1996). Understanding Statistics: Oxford University Press.

Sheet1

Restaurant A Restaurant B

Range 44 46

Variance 260.79-285.64

Std 16.15-16.90

Ttest 0.72

Sheet2

Sheet3

Sheet1

Salary Mid interval salary, x x2 Employees, f f.x f. x2

5001-10000 7500.5 56257500.25-14 105007 787605003.50

10001-15000 12500.5 156262500.25-13 162506.5 2031412503.25

15001-20000 17500.5 306267500.25-18 315009 5512815004.50

20001-25000 22500.5 506272500.25-18 405009 9112905004.50

25001-30000 27500.5 756277500.25-17 467508.5 12856717504.25

Sum ?f ?fx ?fx2

80 1455040 30301455020.00

Mean 18188

Variance 47964843.75

Sheet2

Sheet3

Sheet1

Stores Cost of CD Restaurant A Restaurant B. Salary Mid interval salary, x x 2 Employees, f f.x f. x 2

1 298-120-115 5001-10000 7500.5 56257500.25-14 105007 787605003.50

2 125-123-126 10001-15000 12500.5 156262500.25-13 162506.5 2031412503.25

3 411-153-147 15001-20000 17500.5 306267500.25-18 315009 5512815004.50

4 157-128-156 20001-25000 22500.5 506272500.25-18 405009 9112905004.50

5 231-124-118 25001-30000 27500.5 756277500.25-17 467508.5 12856717504.25

6 213-118-110 Sum ?f ?fx ?fx 2

7 304-154-145 80 1455040 30301455020.00

8 272-110-137 Mean 18188

Std 90.72 Max 154-156 Variance 47964843.75

Min 110-110 Std 6925.6655817329

Range 44 46

Variance 260.79-285.64

Std 16.15-16.90

Waiting time Mid interval time, x x 2 Customers, f f.x f. x 2 Height Mid interval height, x x 2 Customers, f f.x f. x 2

0-3-1.5-2.25-13-19.5-29.25 70-71-70.5 4970.25 3 211.5 14910.75

4-7-5.5-30.25-16 88-484 72-73-72.5 5256.25 7 507.5 36793.75

8-11 9.5-90.25 8-76-722 74-75-74.5 5550.25-16 1192 88804

12-15-13.5 182.25-11-148.5 2004.75 76-77-76.5 5852.25-12-918 70227

16-19-17.5 306.25 0-0-0 78-79-78.5 6162.25-10-785 61622.5

20-23-21.5 462.25 2-43-924.5 80-81-80.5 6480.25 4 322 25921