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.

(c) Recalculate the mean and the standard deviation this time using grouped frequency distribution.

(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

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