Question

In: Statistics and Probability

4. Construct a frequency distribution, find the summary statistics (including the quartiles) for customer age, and...

4. Construct a frequency distribution, find the summary statistics (including the quartiles) for customer age, and graph by each type of customer (regular or promotion). Comment on the shape of the distribution for each type and discuss similarities or differences if any. (Think whether you should create an ungrouped or grouped frequency distribution.) Label the graphs completely.

5. Construct a box-and-whisker plot and find the summary statistics (including the quartiles) for net sales by each type of customer (regular or promotion). Make sure that you format the x-axes on each plot and compare the plots using the same scale. Comment on the shape of the distribution for each type and compare.

Customer	Type of Customer	Items	Net Sales	Method of Payment	Gender	Marital Status	Age
1	Regular	1	49.50	Discover	Male	Married	22
2	Promotional	1	112.40	Proprietary Card	Female	Married	26
3	Regular	1	32.50	Proprietary Card	Female	Married	22
4	Promotional	5	110.40	Proprietary Card	Female	Married	18
5	Regular	2	64.00	MasterCard	Female	Married	24
6	Regular	1	54.50	MasterCard	Female	Married	34
7	Promotional	2	88.00	Proprietary Card	Female	Married	20
8	Regular	1	32.50	Visa	Female	Married	30
9	Promotional	2	66.52	Proprietary Card	Female	Married	36
10	Regular	1	54.50	Proprietary Card	Female	Married	26
11	Regular	1	39.50	Proprietary Card	Female	Married	38
12	Promotional	1	41.60	Proprietary Card	Female	Married	30
13	Promotional	9	170.40	Visa	Female	Married	30
14	Promotional	2	74.50	Visa	Female	Married	36
15	Regular	1	59.50	Visa	Male	Single	44
16	Promotional	2	81.40	Proprietary Card	Male	Single	26
17	Promotional	3	104.00	Proprietary Card	Female	Single	32
18	Regular	3	64.50	Discover	Female	Married	30
19	Promotional	2	48.50	MasterCard	Female	Married	22
20	Promotional	6	54.80	Proprietary Card	Female	Married	46
21	Promotional	1	41.60	Proprietary Card	Female	Single	18
22	Promotional	4	80.82	Proprietary Card	Female	Married	28
23	Promotional	7	276.00	American Express	Female	Married	40
24	Regular	2	84.00	Proprietary Card	Female	Married	32
25	Promotional	2	49.50	Visa	Male	Married	38
26	Promotional	1	40.02	Proprietary Card	Female	Married	50
27	Regular	1	54.50	Proprietary Card	Female	Married	44
28	Promotional	5	202.80	Proprietary Card	Female	Single	32
29	Promotional	3	81.20	Proprietary Card	Female	Married	22
30	Promotional	1	28.00	Proprietary Card	Female	Married	60
31	Promotional	2	73.20	MasterCard	Female	Married	18
32	Regular	1	85.00	Proprietary Card	Female	Married	42
33	Promotional	3	73.20	Proprietary Card	Female	Married	34
34	Regular	1	50.00	Proprietary Card	Female	Married	24
35	Promotional	5	115.50	MasterCard	Female	Married	46
36	Regular	1	39.50	MasterCard	Male	Single	26
37	Regular	2	112.50	Visa	Female	Single	32
38	Promotional	6	127.50	Proprietary Card	Female	Married	40
39	Promotional	5	23.23	Proprietary Card	Female	Married	34
40	Regular	2	62.50	Proprietary Card	Female	Married	48
41	Promotional	13	208.80	Proprietary Card	Female	Married	32
42	Promotional	4	29.50	Visa	Female	Married	36
43	Regular	2	133.50	Proprietary Card	Female	Married	38
44	Promotional	1	72.40	Proprietary Card	Female	Married	44
45	Promotional	2	33.80	Proprietary Card	Female	Married	28
46	Promotional	2	49.60	Proprietary Card	Female	Married	50
47	Regular	1	35.00	MasterCard	Female	Married	36
48	Promotional	3	73.64	Proprietary Card	Female	Married	20
49	Promotional	1	24.82	Proprietary Card	Female	Married	22
50	Promotional	9	155.20	MasterCard	Female	Married	36
51	Promotional	6	186.62	Proprietary Card	Female	Married	28
52	Promotional	5	128.80	Proprietary Card	Male	Married	58
53	Regular	1	68.00	Discover	Female	Single	68
54	Regular	2	84.00	Visa	Female	Single	84
55	Regular	2	59.50	MasterCard	Female	Married	22
56	Promotional	3	151.60	Proprietary Card	Female	Married	28
57	Promotional	6	133.10	Proprietary Card	Female	Married	44
58	Promotional	2	90.40	Proprietary Card	Female	Married	38
59	Promotional	4	75.20	MasterCard	Female	Married	36
60	Promotional	4	123.00	Proprietary Card	Female	Single	40
61	Promotional	1	118.80	Proprietary Card	Female	Married	36
62	Promotional	3	69.91	Proprietary Card	Female	Single	20
63	Promotional	5	63.60	Proprietary Card	Female	Married	44
64	Promotional	1	41.60	Proprietary Card	Female	Single	32
65	Promotional	2	59.50	Proprietary Card	Female	Married	38
66	Promotional	1	49.60	Proprietary Card	Female	Married	52
67	Promotional	2	69.50	Proprietary Card	Female	Married	24
68	Promotional	5	156.80	Proprietary Card	Female	Married	18
69	Promotional	2	57.20	Proprietary Card	Male	Married	36
70	Promotional	8	105.05	Proprietary Card	Female	Married	44
71	Promotional	5	165.32	Proprietary Card	Female	Married	20
72	Promotional	4	68.00	MasterCard	Female	Married	22
73	Regular	1	79.00	Proprietary Card	Female	Single	54
74	Promotional	2	56.50	Proprietary Card	Female	Married	22
75	Promotional	2	55.22	Proprietary Card	Female	Married	64
76	Promotional	4	94.74	Proprietary Card	Female	Married	52
77	Regular	2	49.00	Proprietary Card	Female	Married	32
78	Promotional	4	121.14	Proprietary Card	Female	Married	18
79	Promotional	3	96.80	Proprietary Card	Female	Married	28
80	Regular	2	99.00	Discover	Female	Married	44
81	Promotional	2	88.00	MasterCard	Female	Married	58
82	Promotional	6	63.20	Proprietary Card	Female	Single	20
83	Promotional	4	68.50	Visa	Female	Married	26
84	Promotional	3	56.00	Proprietary Card	Female	Married	34
85	Regular	2	47.50	Visa	Female	Married	34
86	Promotional	1	30.80	Proprietary Card	Female	Married	52
87	Regular	6	154.00	MasterCard	Female	Single	38
88	Regular	4	117.00	Proprietary Card	Female	Married	26
89	Promotional	1	41.60	Proprietary Card	Female	Single	50
90	Promotional	6	67.60	Proprietary Card	Female	Married	32
91	Promotional	4	105.20	Proprietary Card	Female	Married	44
92	Promotional	1	32.42	Proprietary Card	Female	Married	44
93	Regular	5	169.75	Proprietary Card	Female	Married	62
94	Promotional	17	239.50	Proprietary Card	Female	Married	20
95	Regular	3	76.00	American Express	Female	Married	36
96	Regular	1	49.50	MasterCard	Female	Married	34
97	Promotional	9	263.00	Proprietary Card	Female	Married	20
98	Promotional	10	297.59	Proprietary Card	Female	Married	42
99	Promotional	2	57.60	Proprietary Card	Female	Married	20
100	Promotional	1	38.44	Proprietary Card	Female	Married	34

Expert Solution

Question 4:

The summary statistics are:

	Age
count	100
mean	35.14
sample standard deviation	12.67
sample variance	160.51
minimum	18
maximum	84
range	66

1st quartile	26.00
median	34.00
3rd quartile	44.00
interquartile range	18.00
mode	36.00

low extremes	0
low outliers	0
high outliers	1
high extremes	0

The frequency distribution is:

	*Age*						cumulative
lower		upper	midpoint	width	frequency	percent	frequency	percent
10	<	19.99	15	10	5	5.0	5	5.0
20	<	29.99	25	10	30	30.0	35	35.0
30	<	39.99	35	10	34	34.0	69	69.0
40	<	49.99	45	10	17	17.0	86	86.0
50	<	59.99	55	10	9	9.0	95	95.0
60	<	69.99	65	10	4	4.0	99	99.0
70	<	79.99	75	10	0	0.0	99	99.0
80	<	89.99	85	10	1	1.0	100	100.0

					100	100.0

The graph is:

The data is skewed for both types of customers (regular or promotion).

Question 5:

The box-and-whisker plot is:

The summary statistics are:

	Net Sales
count	100
mean	87.6005
sample standard deviation	55.6649
sample variance	3,098.5854
minimum	23.23
maximum	297.59
range	274.36

1st quartile	49.6000
median	69.7050
3rd quartile	110.9000
interquartile range	61.3000
mode	41.6000

low extremes	0
low outliers	0
high outliers	4
high extremes	1

The data is skewed for both types of customers (regular or promotion).

orchestra answered 2 years ago

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