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The frequency distribution below summarizes the batting averages of a sample of Major League Baseball players: Batting Average Frequency 0.160-0.180...

1.The frequency distribution below summarizes the batting averages of a sample of Major League Baseball players:

Batting Average Frequency
0.160-0.180 2
0.180-0.200 4
0.200-0.220 9
0.220-0.240 12
0.240-0.260 13
0.260-0.280 32
0.280-0.300 41
0.300-0.320 22
0.320-0.340 8

(a) What is the relative frequency (i.e., proportion) of observations falling in the 0.260-0.280 interval? (Give your answer to four decimal places.)
(b) What is the shape of the data distribution?
(c) Which is greater -- the median or the mean?
d) Which interval contains the first quartile of data values?

2. A department store is implementing a loyalty card. Customers will earn "points" based on the dollar value of their purchases. The store will offer a signing incentive of 135 points every month and 0.26 points for every dollar the customer spends using their loyalty card. The following is the amount spent by a customer during the first 6-months with their loyalty card.

101.48 136.73 120.78 99.26 118.08 96.68

** all answers should be to two decimal places.**

(a) The mean amount spent by the customer is $ and the standard devation of the amounts spent by the customer is $ .

(b) The mean number of loyalty points earned by the customer is and the standard deviation of the loyalty points earned is
(Hint: You don't need to convert every observation, you can just use your results from part (a)).

(c) Data was then gathered for a seventh month and it was found the customer spent $112.17. The mean amount spent by the customer over the 7-month period is $ .

(d) What would happen to the standard deviation of the amounts spend by the customer when this seventh observation is included?

3. We asked 15 students at the University of Manitoba, "How many songs are on your iTunes playlist?" The results are shown in the table below:

4141 4760 4413 3420 3400 4978 4406 4298 4066 3896 4678 5100 4916 3631 6018

(a) Find the five-number summary for this dataset (do not use JMP, it calculates the quartiles differently).

(b) If we were to construct a modified (outlier) boxplot of this dataset, an observation would be labeled an outlier if it was less than or greater than .

4. A male and female server at a very expensive steakhouse wanted to see how their tip percentages compare. The following are their tip percentages for each table they waited on over the course of one evening:

Male Tip % Female Tip %
30 65
13 21
9 28
20 33
9 27
22 25
22 34
15 40
14 23
14 17
12 24
16 24
17 27
18 30
17 21
15 29
15 41
18 22
19 33
27 72
24 45

(a) Construct a back-to-back stemplot.

(b) Use JMP to construct two histograms (in horizontal layout) for this dataset. To do this, enter the data in one column titled "Male Tip %". Go to Analyze > Distribution. Click Male Tip %, then Y, Columns and OK. Then, enter the data in a second column titled "Female Tip %". Go to Analyze > Distribution. Click Female Tip %, then Y, Columns and OK. Under the red arrow, you can remove the boxplot and numerical summaries leaving only the histogram, but this isn't necessary. Now attach the histogram to your assignment.

***NOTE: You MUST follow the proper instructions for attaching an image to your assignment. Copying and pasting the image or dragging and dropping it WILL NOT WORK. (It will show up in your window, but when you submit your assignment, the marker will NOT be able to see it.) If you need a reminder how to attach an image to your assignment, see Assignment 0, Question 8.

(c) Using JMP, create side-by-side boxplots comparing the distributions of returns for the two sectors. To do this, create a new data table with two columns called Tip % and Gender. In the first column, enter all 45 tip % (first the 22 female tip % and then the 23 male tip %). In the second column, type "Female" in the first 22 cells and "Male" in the next 23 cells. Go to Analyze > Fit Y by X. Choose Tip % as Y and Gender as X. Click OK. Now, under the red arrow, select Quantiles. Also under the red arrow in Display Options, remove the points and the line for the grand mean. Attach your graph to your assignment.

(d) Compare the two distributions with respect to center, shape and spread.

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