CASE ASSIGNMENT FOR BASIC STATISTICS

Case Assignment for Basic Statistics



Case Assignment for Basic Statistics

Question 1

 

CD Player Prices in $

 

N

X

X2

1

298

88804

2

125

15625

3

411

168921

4

157

24649

5

231

53361

6

213

45369

7

304

92416

8

272

73984

 

 

563129

Mean =

sum of all observations

No. of observations

Mean =

(298 + 125 + 411 + 157 + 231 + 213 + 304 + 272)

8

Mean =

2011

8

Mean =

$ 251.38

Square of Mean =

(251.38)2

Square of Mean =

63,189.4

Variance = (X2/n) - Mean square

Variance =

563129

-

63,189.4

8

Variance =

70391.1

-

63,189.4

Variance =

7201.7

Standard Deviation = Square Root of Variance

Standard Deviation = Square Root (7201.7)

Standard Deviation = 84.86

Standard Deviation on CD player prices from eight appliances store is $84.86.

Question 2

Drive Through Service

N

Restaurant A

X2

Restaurant B

X2

1

120

14400

115

13225

2

123

15129

126

15876

3

153

23409

147

21609

4

128

16384

156

24336

5

124

15376

118

13924

6

118

13924

110

12100

7

154

23716

145

21025

8

110

12100

137

18769

 

1030

134438

1054

140864

 

Restaurant A

Restaurant B

Mean =

1030

 

1054

 

 

8

 

8

 

Mean =

128.75

seconds

131.75

seconds

 

 

 

 

Square of Mean =

(128.75)2

 

(131.75)2

 

Square of Mean =

16576.56

 

17358.06

 

 

Restaurant A

Restaurant B

Max

154

156

Min

110

110

Range

44

46

 

Restaurant A

Restaurant B

Variance =

134438

-

16,576.6

140864

-

17,358.1

 

8

 

8

 

 

 

 

 

Variance =

16804.8

-

16,576.6

17608

-

17,358.1

Variance =

228.2

 

249.94

 

 

 

 

 

Standard Deviation=

15.11

 

 

15.81

 

 

Standard Deviation of restaurant A is 15.11 seconds for drive through service; whereas, standard Deviation of restaurant A is 15.81 seconds for drive through service. Results show that drive through service of restaurant A is quicker than restaurant B. Minimum time for drive-through service of 110 seconds is equal for both restaurants; however, maximum time for drive-through service is 154 seconds at restaurant A, whereas, it is 156 seconds at restaurant B.

Question 3

Interval

Mid Point (X)

F

F X

X2

F X2

5001

10000

7500.5

14

105007

56257500

787605003.5

10001

15000

12500.5

13

162507

156262500

2031412503

15001

20000

17500.5

18

315009

306267500

5512815005

20001

25000

22500.5

18

405009

506272500

9112905005

25001

30000

27500.5

17

467509

756277500

12856717504

Total

 

 

80

1455040

 

30301455020

Mean =

1455040

 

 

80

 

Mean =

18188

dollars

 

 

Square of Mean =

(18188)2

 

Square of Mean =

330803344

 

Variance =

30301455020

-

330,803,344

 

80

 

 

 

Variance =

378768187

-

330,803,344

Variance =

47964843

 

 

 

Standard Deviation=

6925.67

 

 

Standard deviation in salary of employees is 6925.67 dollars.

Question 4

Interval

Mid Point (X)

F

F X

X2

F X2

0

3

1.5

13

20

2

29

4

7

5.5

16

88

30

484

8

11

9.5

8

76

90

722

12

15

13.5

11

149

182

2005

16

19

17.5

0

0

306

0

20

23

21.5

2

43

462

925

Total

 

 

50

375

 

4165

Mean =

375

 

 

50

 

Mean =

7.5

minutes

 

 

Square of Mean =

(7.5)2

 

Square of Mean =

56

 

Variance =

4164.5

-

56.25

 

50

 

 

 

 

Variance =

83.3

-

56.25

Variance =

27.0

 

 

 

 

Standard Deviation=

5.20

 

 

Standard deviation between customer's waiting in line during peak business hours is 5.20 minutes.

Question 5

Interval

Mid Point (X)

F

F X

X2

F X2

70

71

70.5

3

212

4970

14911

4

73

38.5

7

270

1482

10376

74

75

74.5

16

1192

5550

88804

76

77

76.5

12

918

5852

70227

78

79

78.5

10

785

6162

61623

80

81

80.5

4

322

6480

25921

82

83

82.5

1

83

6806

6806

Total

 

 

53

3780.5

 

278667

Mean =

3780.5

 

 

53

 

Mean =

71.33018868

inches

 

 

Square of Mean =

(7.5)2

 

Square of Mean =

5088

 

Variance =

278667.25

-

5088

 

53

 

 

 

 

Variance =

5257.9

-

5088

Variance =

169.9

 

 

 

 

Standard Deviation=

13.03

 

 

Standard deviation in the height of a group of professional basketball players is 13.03 inches.

PART II

(1)

In the above stated scenario, first of all stratified sampling technique has been used the resulted in grouping of students in three categories. These include Junior, Sophomore, and Senior classes' students. After that “systematic random sampling technique” has been used in which first student from every sample group is selected at random. After that, every 10th student is selected from the strata of homogenous but exclusive groups. This resulted in selection of 10% of students from each group. This is done to ensure that every participant has equal ...