Solution Library

Calculate Mean, Standard Deviation And Use Sterges’ 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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Comments

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