read the scenario and answer the questions

Scenario:

Pastas R Us, Inc. is a fast-casual restaurant chain specializing in noodle-based dishes, soups, and salads. Since its inception, the business development team has favored opening new restaurants in areas (within a 3-mile radius) that satisfy the following demographic conditions:

Median age between 25 – 45 years old

Household median income above national average

At least 15% college educated adult population

Last year, the marketing department rolled out a Loyalty Card strategy to increase sales. Under this program, customers present their Loyalty Card when paying for their orders and receive some free food after making 10 purchases.

The company has collected data from its 74 restaurants to track important variables such as average sales per customer, year-on-year sales growth, sales per sq. ft., Loyalty Card usage as a percentage of sales, and others. A key metric of financial performance in the restaurant industry is annual sales per sq. ft. For example, if a 1200 sq. ft. restaurant recorded $2 million in sales last year, then it sold $1,667 per sq. ft.

Executive management wants to know whether the current expansion criteria can be improved. They want to evaluate the effectiveness of the Loyalty Card marketing strategy and identify feasible, actionable opportunities for improvement. As a member of the analytics department, you’ve been assigned the responsibility of conducting a thorough statistical analysis of the company’s available database to answer executive management’s questions.

Questions

In preparation for writing your report to senior management next week, conduct the following descriptive statistics analyses with Microsoft® Excel®. Answer the questions below in your Microsoft® Excel® sheet or in a separate Microsoft® Word document:

Insert a new column in the database that corresponds to “Annual Sales.” Annual Sales is the result of multiplying a restaurant’s “SqFt.” by “Sales/SqFt.”

Calculate the mean, standard deviation, skew, 5-number summary, and interquartile range (IQR) for each of the variables.

Create a box-plot for the “Annual Sales” variable. Does it look symmetric? Would you prefer the IQR instead of the standard deviation to describe this variable’s dispersion? Why?

Create a histogram for the “Sales/SqFt” variable. Is the distribution symmetric? If not, what is the skew? Are there any outliers? If so, which one(s)? What is the “SqFt” area of the outlier(s)? Is the outlier(s) smaller or larger than the average restaurant in the database? What can you conclude from this observation?

What measure of central tendency is more appropriate to describe “Sales/SqFt”? Why?

Resources

Pastas R Us, Inc. Database

Pastas R Us, Inc. Database (n = 74 restaurants)
Per Person Sales Growth Over Loyalty Card % of Annual Sales
Square Feet Average Spending Previous Year (%)
Net Sales
Per Sq Ft
Obs
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
SqFt
2354
2604
2453
2340
2500
2806
2250
2400
2709
1990
2392
2408
2627
2500
1986
2500
2668
2517
1251
2998
2625
2300
2761
2764
2430
2154
2400
2430
2549
2500
3653
Sales/Person
6.81
7.57
6.89
7.13
7.04
6.93
7.11
7.13
6.58
6.77
6.66
7.03
7.03
7.00
7.38
7.18
7.35
6.95
7.02
6.85
7.16
6.99
7.28
7.07
7.05
6.54
6.70
6.91
7.58
7.03
6.84
Noodles Database – Page 1 of 3
SalesGrowth%
-8.31
-4.01
-3.94
-3.39
-3.30
-1.94
-0.77
-0.37
-0.25
-0.17
0.47
0.55
0.77
1.92
2.05
2.12
2.84
2.88
3.96
4.04
4.05
4.05
4.24
4.58
5.09
5.14
5.48
5.86
5.91
5.98
6.08
LoyaltyCard%
2.07
2.54
1.66
2.06
2.48
2.96
2.28
2.34
2.20
2.34
2.09
2.47
2.04
2.02
2.01
2.64
2.22
2.07
1.94
2.17
0.72
2.00
1.81
2.13
2.50
2.63
1.95
2.04
1.41
2.05
2.13
Sales/SqFt
701.97
209.93
364.92
443.04
399.20
264.64
571.59
642.25
461.45
638.82
484.38
581.09
267.71
572.84
586.48
368.73
351.47
458.24
987.12
357.45
405.77
680.80
368.02
303.95
393.90
562.12
494.88
310.07
373.46
235.81
413.08
Printed 12/6/2022
Median HH
Income (3 Miles)
MedIncome
45177
51888
51379
66081
50999
41562
44196
50975
72808
79070
78497
41245
33003
90988
37950
45206
79312
37345
46226
70024
54982
54932
34097
46593
51893
88162
89016
114353
75366
48163
49956
Median Age % w/ Bachelor’s
(3 Miles) Degree (3 Miles)
MedAge
34.4
41.2
40.3
35.4
31.5
36.3
35.1
37.6
34.9
34.8
36.2
32.2
30.9
37.7
34.3
32.4
32.1
31.4
30.4
33.9
35.6
35.9
33.6
37.9
40.6
37.7
36.4
40.9
35.0
26.4
37.1
BachDeg%
31
20
24
29
18
30
14
33
28
29
39
23
22
37
24
17
37
22
36
34
26
20
20
26
21
37
34
34
30
16
28
Doane/Seward
Pastas R Us, Inc. Database (n = 74 restaurants)
Per Person Sales Growth Over Loyalty Card % of Annual Sales
Square Feet Average Spending Previous Year (%)
Net Sales
Per Sq Ft
Obs
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
SqFt
2440
2600
2160
2800
2757
2450
2400
2270
2800
2520
2487
2629
3200
2335
2500
2449
2625
3150
2625
2741
2500
2450
2986
2967
3000
2500
2600
2800
2986
2223
2300
Sales/Person
6.94
7.07
7.00
7.08
6.75
6.81
7.64
6.62
6.76
7.11
7.05
6.90
7.17
6.75
7.45
7.00
6.96
7.30
6.96
6.71
6.82
6.58
7.56
6.98
7.28
6.76
6.92
6.73
6.91
6.77
7.33
Noodles Database – Page 2 of 3
SalesGrowth%
6.08
6.13
6.27
6.57
6.90
6.94
7.12
7.39
7.67
7.91
8.08
8.27
8.54
8.58
8.72
8.75
8.79
8.90
9.12
9.47
10.17
10.66
10.97
11.34
11.45
11.51
11.73
11.83
11.95
12.47
12.80
LoyaltyCard%
2.08
2.73
1.95
2.04
1.62
1.95
1.64
1.78
2.23
2.15
2.83
2.37
3.07
2.19
1.28
1.76
2.51
1.90
1.98
2.41
2.17
2.16
0.29
1.85
1.88
2.19
2.56
2.16
2.10
1.98
0.87
Sales/SqFt
625.22
274.30
542.62
178.56
375.33
329.09
297.37
323.17
468.84
352.57
380.34
398.12
312.15
452.16
698.64
367.19
431.93
367.06
400.53
414.36
481.11
538.06
330.48
249.93
291.87
517.40
551.58
386.81
427.50
453.94
512.46
Printed 12/6/2022
Median HH
Income (3 Miles)
MedIncome
45990
45723
43800
68711
65150
39329
63657
67099
75151
93876
79701
77115
52766
32929
87863
73752
85366
39180
56077
77449
56822
80470
55584
78001
75307
76375
61857
61312
72040
92414
92602
Median Age % w/ Bachelor’s
(3 Miles) Degree (3 Miles)
MedAge
30.3
31.3
29.6
32.9
40.7
29.3
37.3
39.8
33.9
35.0
35.0
35.9
33.0
30.9
38.5
40.5
32.1
34.8
38.0
37.0
34.7
36.4
36.8
32.2
34.8
36.7
33.8
34.2
39.0
34.9
39.3
BachDeg%
36
18
36
18
24
22
29
25
28
40
39
30
17
22
29
19
29
18
19
34
25
30
21
30
30
28
31
16
31
40
33
Doane/Seward
Pastas R Us, Inc. Database (n = 74 restaurants)
Per Person Sales Growth Over Loyalty Card % of Annual Sales
Square Feet Average Spending Previous Year (%)
Net Sales
Per Sq Ft
Obs
63
64
65
66
67
68
69
70
71
72
73
74
SqFt
3799
2700
2650
2500
2994
2718
3700
2000
2400
2450
2575
2400
Sales/Person
7.87
6.95
7.33
6.95
7.21
7.25
7.65
6.93
6.79
7.37
6.76
7.97
Noodles Database – Page 3 of 3
SalesGrowth%
13.78
14.09
14.23
14.60
14.88
15.42
16.18
17.23
18.43
20.76
25.54
28.81
LoyaltyCard%
1.07
3.38
1.17
2.14
0.93
2.22
1.68
2.41
2.81
1.09
0.64
1.77
Sales/SqFt
345.27
234.04
348.33
348.47
294.95
361.14
467.71
403.78
245.74
339.94
400.82
326.54
Printed 12/6/2022
Median HH
Income (3 Miles)
MedIncome
59599
72453
67925
42631
75652
39650
48033
67403
80597
60928
73762
64225
Median Age % w/ Bachelor’s
(3 Miles) Degree (3 Miles)
MedAge
35.6
36.0
41.1
24.7
40.5
32.9
30.3
36.2
32.4
43.5
41.6
31.4
BachDeg%
28
23
16
25
25
18
15
19
27
21
29
15
Doane/Seward