Variability, Variance, Mean, Mode, Standard Deviation


1.      Compare the variability of the following two sets of data by using both the population standard deviation and the population coefficient of variation.

 

Data Set 1

Data Set 2

 

49

159

 

82

121

 

77

138

 

54

152

σ2 =

809

845

σ  =

28.44293

29.06888

CV =

0.434243 = 3.4%

0.203992 = 20.4%

 

2.      A random sample of voters in Nashville, Tennessee is classified by age group as shown by the following data.

Age Group

Frequency

18-under 24

17

24-under 30

22

30-under 36

26

36-under 42

35

42-under 48

33

48-under 54

30

54-under 60

32

60-under 66

21

66-under 72

15

 

 

f

Midpoint (M)

fM

fM2

variance

std dev.

18-under 24

17

(24+18)/2 = 21

357

7497

186.3788

13.65206

24-under 30

22

(24+30)/2 = 27

594

16038

 

 

30-under 36

26

(30+36)/2 = 33

858

28314

 

 

36-under 42

35

(36+42)/2 = 39

1365

53235

42-under 48

33

(42+48)/2 = 45

1485

66825

48-under 54

30

(48+54)/2 = 51

1530

78030

54-under 60

32

(54+60)/2 = 57

1824

103968

60-under 66

21

(60+66)/2 = 63

1323

83349

 

 

66-under 72

15

(66+72)/2 = 69

1035

71415

 

 

 

 

 

10371

508671