Calculate Mean, Standard Deviation And Use Stergesâ€™ Rule To Calculate Number Of Classes

Question

Pelican Stores is a chain of women’s apparel stores operating through this country. The chain recently ran a promotion in which discount coupons were sent to customers of related stores. Data collected for a sample of 100 in-store credit transactions during one day in November of 2006 are contained in the file.

Customer	Method of Payment	Items	Discount	Sales	Gender	Marital Status	Age
1	Discover	1	0.00	39.50	Male	Married	32
2	Proprietary Card	1	25.60	102.40	Female	Married	36
3	Proprietary Card	1	0.00	22.50	Female	Married	32
4	Proprietary Card	5	121.10	100.40	Female	Married	28
5	Mastercard	2	0.00	54.00	Female	Married	34
6	Mastercard	1	0.00	44.50	Female	Married	44
7	Proprietary Card	2	19.50	78.00	Female	Married	30
8	Visa	1	0.00	22.50	Female	Married	40
9	Proprietary Card	2	22.48	56.52	Female	Married	46
10	Proprietary Card	1	0.00	44.50	Female	Married	36
11	Proprietary Card	1	0.00	29.50	Female	Married	48
12	Proprietary Card	1	7.90	31.60	Female	Married	40
13	Visa	9	103.60	160.40	Female	Married	40
14	Visa	2	24.50	64.50	Female	Married	46
15	Visa	1	0.00	49.50	Male	Single	24
16	Proprietary Card	2	12.60	71.40	Male	Single	36
17	Proprietary Card	3	53.00	94.00	Female	Single	22
18	Discover	3	0.00	54.50	Female	Married	40
19	Mastercard	2	19.00	38.50	Female	Married	32
20	Proprietary Card	6	32.20	44.80	Female	Married	56
21	Proprietary Card	1	7.90	31.60	Female	Single	28
22	Proprietary Card	4	29.67	70.82	Female	Married	38
23	American Express	7	66.50	266.00	Female	Married	50
24	Proprietary Card	2	0.00	74.00	Female	Married	42
25	Visa	2	14.50	39.50	Male	Married	48
26	Proprietary Card	1	9.48	30.02	Female	Married	60
27	Proprietary Card	1	0.00	44.50	Female	Married	54
28	Proprietary Card	5	48.20	192.80	Female	Single	42
29	Proprietary Card	3	37.30	71.20	Female	Married	32
30	Proprietary Card	1	4.50	18.00	Female	Married	70
31	Mastercard	2	15.80	63.20	Female	Married	28
32	Proprietary Card	1	0.00	75.00	Female	Married	52
33	Proprietary Card	3	15.80	63.20	Female	Married	44
34	Proprietary Card	1	0.00	40.00	Female	Married	34
35	Mastercard	5	10.00	105.50	Female	Married	56
36	Mastercard	1	0.00	29.50	Male	Single	36
37	Visa	2	0.00	102.50	Female	Single	42
38	Proprietary Card	6	14.50	117.50	Female	Married	50
39	Proprietary Card	5	25.02	13.23	Female	Married	44
40	Proprietary Card	2	0.00	52.50	Female	Married	58
41	Proprietary Card	13	62.70	198.80	Female	Married	42
42	Visa	4	16.50	19.50	Female	Married	46
43	Proprietary Card	2	0.00	123.50	Female	Married	48
44	Proprietary Card	1	15.60	62.40	Female	Married	54
45	Proprietary Card	2	35.20	23.80	Female	Married	38
46	Proprietary Card	2	19.40	39.60	Female	Married	60
47	Mastercard	1	0.00	25.00	Female	Married	46
48	Proprietary Card	3	20.11	63.64	Female	Married	30
49	Proprietary Card	1	4.68	14.82	Female	Married	32
50	Mastercard	9	94.30	145.20	Female	Married	46
51	Proprietary Card	6	58.88	176.62	Female	Married	38
52	Proprietary Card	5	51.70	118.80	Male	Married	68
53	Discover	1	0.00	58.00	Female	Single	78
54	Visa	2	0.00	74.00	Female	Single	20
55	Mastercard	2	0.00	49.50	Female	Married	32
56	Proprietary Card	3	35.40	141.60	Female	Married	38
57	Proprietary Card	6	56.40	123.10	Female	Married	54
58	Proprietary Card	2	20.10	80.40	Female	Married	48
59	Mastercard	4	28.30	65.20	Female	Married	46
60	Proprietary Card	4	19.50	113.00	Female	Single	50
61	Proprietary Card	1	19.20	108.80	Female	Married	46
62	Proprietary Card	3	91.48	59.91	Female	Single	30
63	Proprietary Card	5	37.40	53.60	Female	Married	54
64	Proprietary Card	1	7.90	31.60	Female	Single	42
65	Proprietary Card	2	9.50	49.50	Female	Married	48
66	Proprietary Card	1	9.90	39.60	Female	Married	62
67	Proprietary Card	2	29.50	59.50	Female	Married	34
68	Proprietary Card	5	36.70	146.80	Female	Married	28
69	Proprietary Card	2	11.80	47.20	Male	Married	46
70	Proprietary Card	8	18.95	95.05	Female	Married	54
71	Proprietary Card	5	57.18	155.32	Female	Married	30
72	Mastercard	4	10.00	58.00	Female	Married	32
73	Proprietary Card	1	0.00	69.00	Female	Single	22
74	Proprietary Card	2	15.50	46.50	Female	Married	32
75	Proprietary Card	2	14.28	45.22	Female	Married	74
76	Proprietary Card	4	46.26	84.74	Female	Married	62
77	Proprietary Card	2	0.00	39.00	Female	Married	42
78	Proprietary Card	4	35.11	111.14	Female	Married	28
79	Proprietary Card	3	31.20	86.80	Female	Married	38
80	Discover	2	0.00	89.00	Female	Married	54
81	Mastercard	2	19.50	78.00	Female	Married	68
82	Proprietary Card	6	29.31	53.20	Female	Single	30
83	Visa	4	14.50	58.50	Female	Married	36
84	Proprietary Card	3	19.50	46.00	Female	Married	44
85	Visa	2	0.00	37.50	Female	Married	44
86	Proprietary Card	1	5.20	20.80	Female	Married	62
87	Mastercard	6	0.00	144.00	Female	Single	48
88	Proprietary Card	4	0.00	107.00	Female	Married	36
89	Proprietary Card	1	7.90	31.60	Female	Single	20
90	Proprietary Card	6	46.40	57.60	Female	Married	42
91	Proprietary Card	4	158.30	95.20	Female	Married	54
92	Proprietary Card	1	7.08	22.42	Female	Married	54
93	Proprietary Card	5	0.00	159.75	Female	Married	72
94	Proprietary Card	17	33.00	229.50	Female	Married	30
95	American Express	3	0.00	66.00	Female	Married	46
96	Mastercard	1	0.00	39.50	Female	Married	44
97	Proprietary Card	9	82.75	253.00	Female	Married	30
98	Proprietary Card	10	18.00	287.59	Female	Married	52
99	Proprietary Card	2	31.40	47.60	Female	Married	30
100	Proprietary Card	1	11.06	28.44	Female	Married	44

1. Using “method of payment” as your variable,

(a) make percent frequency distribution table. How would you classify these data?

(b) make a pie graph for the method of payments and state why is it an appropriate graph in this situation.

2. Use “age” as your new variable now. What type of data is it?

(a) Calculate the mean and the standard deviation using raw data.

(b) Create grouped frequency distribution for these data. Use Sterges’s rule to calculate an appropriate number of classes.

(d) Using original data, find the values of the median, first and third quartiles (don’t use excel for this question, it does not provide correct results)

(e) Make box-and whiskers plot for this variable, comment on the shape of the distribution.

(f) Make a table to show what percent of data lies within one, two and three standard deviations of the mean. Compare your results to empirical rule and make your conclusion.

(g) Make a cumulative percentage polygon for these data. What does this graph describe?

(h) If you were the manager of one of the chain’s store, what practical conclusion would you draw from these data analysis?

(i) If the ages of the customers are normally distributed with the mean of 45 years and the standard deviation of 12 years, find:

1) what present of customers are between 35 and 50 years old?

2) what is the minimum age of the oldest 12 % of the customers?

Summary

The question belongs to Statistics and it discusses about making frequency distribution table, pie graph and calculate mean, standard deviation and use Sterges’ rule to calculate appropriate number of classes for the given data.

Total Word Count 709