Descriptive Statistics and Sampling



Descriptive Statistics and Sampling

Question 1 Solution

CD Player Deals

(Purchase Price in Dollars)

S. No.

x

x2

1

298

88804

2

125

15625

3

511

261121

4

157

24649

5

231

53361

6

230

52900

7

304

92416

8

272

73984

 

 

662860

Mean CD Player Price =(total sum of all observations) / total number of observations

Mean CD Player Price =(298 + 125 + 411 + 157 + 231 + 213 + 304 + 272) / 8

Mean CD Player Price =2128 / 8

Mean CD Player Price =$266

Variance = (Sum of X2 / n) - Square of Mean

Sum of X2 =662860

N= 8

Square of Mean =(251.38)2

Square of Mean = 70,756.0

Variance = (662860 / 8) - 70,756.0

Variance = 82857.5 - 70,756.0

Variance = 12101.5

Standard Deviation =Square Root of Variance

Standard Deviation =110.01

Above presented calculation shows that the standard Deviation on CD player deal prices obtained from eight appliances store is $110.01.

Question 2 Solution

Restaurant A & B Drive-Through Service (in Seconds)

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

Range of Drive-Through Service Time of Restaurant A & B

 

Restaurant A

Restaurant B

Max

154

156

Min

110

110

Range

44

46

Variance and Standard Deviation of Drive-Through Service Time of Restaurant A & B

For Restaurant A

Mean Drive-through Service Time =(total sum of all observations) / total number of observations

Mean Drive-through Service Time =1030 / 8

Mean Drive-through Service Time =128.75 seconds

Variance = (Sum of X2 / n) - Square of Mean

Sum of X2 =134438

N= 8

Square of Mean =(128.75)2

Square of Mean = 16576.56

Variance = (134438 / 8) - 1657.56

Variance = 16804.8 - 1657.56

Variance = 228.2

Standard Deviation =15.11 seconds

For Restaurant B

Mean Drive-through Service Time =(total sum of all observations) / total number of observations

Mean Drive-through Service Time =1054 / 8

Mean Drive-through Service Time =131.75 seconds

Variance = (Sum of X2 / n) - Square of Mean

Sum of X2 =140864

N= 8

Square of Mean =(131.75)2

Square of Mean = 17358.06

Variance = (140864 / 8) - 17358.06

Variance = 17608 - 1657.56

Variance = 249.94

Standard Deviation =15.81 seconds

Results Analysis

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

Question 3 Solution

Employee Salaries 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

Average Salary of an Employee =(total sum of all observations) / total number of observations

Average Salary of an Employee =1455040 / 80

Average Salary of an Employee =18188 dollars

Variance = (Sum of X2 / n) - Square of Mean

Sum of X2 =30301455020

Total Employees= 80

Square of Mean =(18188)2

Square of Mean =330803344

Variance = (30301455020 / 80) - 330803344

Variance = 378768187.8 - 330803344

Variance = 47964843.8

Standard Deviation =6925.67 dollars

Above presented calculation shows that the standard deviation of employees' salaries is $6925.67.

Question 4 Solution

Waiting Time 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 Waiting Time in Line =(total sum of all observations) / total number of observations

Mean Waiting Time in Line =375 / 8

Mean Waiting Time in Line =7.5 min

Variance = (Sum of X2 / n) - Square of Mean

Sum of X2 =4165

N= 50

Square of Mean =(7.5)2

Square of Mean = 56.25

Variance = (4165 / 50) - ...