Case Analysis Ms. Fatima has recently taken over her grandparent's bakery business. She is learning the new business and wants to continue the past success of the bakery which has been in her family for over fifty years. Currently, the bakery's primary products are bread, cakes, cookies, cupcakes, doughnuts, muffins, pies, and rolls. Fatima is curious to see which bakery products are the most popular, the amount a typical customer spends, and how customers would rate the bakery on taste, product selection, and service. Fatima decides to track the primary bakery items purchased and the amount customers spend. In addition, she asks these customers to rate the tastiness of the bakery's products, selection, and service on a scale from one to five with five being the highest and one the lowest. Table 1 shows the data for 75 customers surveyed. For example, Customer 4's main purchase was pies, the customer spent $51.99, and gave taste a 4, selection a 5, and service a 4. Table 1: Customer Data Primary Bakery Item Purchased Total Amount Spent by the Customer Rating for Rating for Product Rating for Taste Selection Service Bread $31.50 5 2 4 Donuts 28.13 3 3 3 Bread 15.43 4 2 4 Pies 41.80 4 5 4 Bread 27.19 4 5 4 Muffins 25.19 3 4 5 Donuts 15.21 2 2 3 Cakes 60.59 4 3 3 Donuts 10.23 4 3 2 Page 2 of 8 Muffins 11.13 4 3 5 Donuts 60.50 5 5 4 Cakes 91.85 1 4. 2Table 1 cont. Bread 31.59 2 5 5 Muffins 40.52 3 2 3 Cakes 82.16 2 2 4 Cookies 11.42 5 5 2 Rolls 24.19 5 5 3 Cookies 20.90 4 1 5 Bread 12.14 3 1 5 Bread 37.62 4 3 4 Cookies 43.69 4 5 4 Rolls 31.53 3 1 1 Bread 27.46 3 2 3 Donuts 35.48 1 5 4 Rolls 19.99 1 5 2 Cakes 55.13 1 5 2 Cupcakes 18.17 2 1 1 Cookies 16.17 4 4 2 Donuts 8.99 2 4 1 Donuts 5.71 5 4 1 Bread 11.98 3 2 2 Pies 58.19 3 5 2 Donuts 10.08 1 4 3 Cakes 57.63 5 5 3 Muffins 32.94 4 5 4 Bread 18.48 4 2. 5 Cakes 79.17 3 2 4 Bread 41.44 1 1 5 Page 4 of 8Table 1 cont. Rolls 6.59 1 1 2 Bread 25.67 4 1 4 Cakes 57.19 5 5 3 Donuts 13.78 3 2 1 Muffins 34.52 2 1 3 Bread 25.74 1 1 3 Cookies 42.73 4 2 4 Bread 21.95 1 3 1 Cookies 31.44 4 1 2 Donuts 6.59 2 4 1 Rolls 18.95 1 4 4 Bread 43.99 3 3 3 Bread 35.89 4 1 2 Rolls 14.59 4 1 5 Cookies 23.25 2 2 5 Donuts 28.46 5 4 3 Donuts 5.46 2 5 3 Cookies 34.72 5 1 5 Cookies 25.83 2 4 2 Cookies 15.78 2 3 5 Muffins 36.76 3 3 5 Rolls 29.99 1 1 3 Donuts 12.98 4 2 5 Cupcakes 33.15 4 5 1 Cupcakes 12.15 1 3 3 Page 5 of 8Table 1 cont. Rolls 30.87 4 3 5 Cakes 64.58 5 4 5 Donuts 23.14 1 3 4 Cookies 12.96 5 2 2 Muffins 5.99 1 3 2 Cakes 67.36 5 2 3 Muffins 43.17 5 1 1 Donuts 14.83 2 2 5 Cookies 43.42 3 2 3 Cookies 17.55 2 5 3 Bread 12.55 4 3 3 Rolls 40.18 4 2 1 In addition, Fatima would like to know how her bakery compares with others. She contacts her cousin, who runs a bakery in another town that sells similar bakery items. Her cousin sends her customer data that is grouped. However, Fatima can find estimates for measures such as the mean and standard deviation. Table 2 contains the frequency distribution of the total amount spent by customers. For example, 13 customers spent between $30.00 to $39.99. Table 2: Total Amount Spent by Customers Frequency 4 18 20 13 Class $0.00 to $9.99 $10.00 to $19.99 $20.00 to $29.99 $30.00 to $39.99 $40.00 to $49.99 $50.00 to $59.99 $60.00 to $69.99 $70.00 to $79.99 $80.00 to $89.99 $90.00 to $99.99 3 5 4 5 2 1 Page 6 of 8Finally, Fatima notices that the bakery usually does monthly promotions and wants to know if there is truly a relationship between the number of promotions and total sales. She gathers data from the past twelve months. Table 3 below provides the number of promotions and total sales for the past twelve months. For example, in Month 3 the total number of promotions was 2 and the total monthly sales was $38,427. Table 3: Number of Promotions and Total Monthly Sales Month Number of Promotions Total Monthly Sales 1 1 $33,581 2 3 37,560 3 2 38,427 4 4 41,850 5 5 43,678 6 3 40,909 7 2 39,500 8 4 42,740 9 6 47,500 10 4 42,593 11 3 43,125 12 5 44,870 REQUIRED: Now that Fatima has all this data, she needs some help organizing and analyzing it. She would like the following included in a report: 1) Primary bakery item purchased (Table 1) ( 25 points) a) Construct a frequency distribution and relative frequency distribution for the data. b) Construct a bar graph and pie chart. (using excel) Page 7 of 8c) Discuss the results of the tables and charts. 2) Total amount spent by customers (Table 1) ( 25 points) a) Construct a frequency distribution and relative frequency distribution for the data. b) Determine the following numerical measures: mean, median, mode, range, sample variance, sample standard deviation, first quartile, third quartile, interquartile range, and the coefficient of variation. c) Discuss the results of the tables, histogram, and numerical measures. 3) Grouped data (Table 2) (15 points) a) Determine the mean and standard deviation for the grouped data. b) Discuss how these numerical measures compare to those found for the total amount spent by customers at Fatima's bakery (Table 1 data). How are they different? 4) Ratings for taste, product selection, and service (Table 1) (15 points) a) Summarize in a table the ratings for taste, product selection, and service. b) Determine the mean for each. c) Discuss the findings. Are there areas for improvement? 5) Total Sales vs. Number of Promotions (Table 3) (20 points) a) Construct a bar diagram for the total sales and the number of promotions data. b) Determine the sample covariance. Page 8 of 8