3.4

z=(x-m)/σ

34 week baby:

x= 2400 (-200)

m= 2600

σ= 660

z= (200-2600)/660 = -3.63

40 week baby:

x= 3300 (-200)

m= 3500

σ= 470

z= (200-3500)/470 = -7.02

The 34 week baby weighs less in relation to it’s gestation period.

man:

x= 75

m= 69.6

σ= 3

z= (75-69.6)/ 3 = 1.8

woman:

x= 70

m= 64.1

σ= 3.8

z= (70-64.1)/ 3.8 = 1.6

The 75 inch man is relatively taller than the woman.

American League

x= 2.27

m= 3.929

σ= 0.775

z= (2.27-3.929)/0.775 = -2.14

National League

x= 2.3

m= 3.622

σ= 0.743

z= (2.3-3.622)/ 0.743 = -1.78

Hernandez had a better year relative to his peers because his z score is a lower number which means its closer to the mean than Johnsons.

Indianapolis

x= 185.62

m= 186.15

σ= 0.359

z= (185.62-186.15)/0.359 = -1.48

Grand Prix

x= 112.57

m= 112.8

σ= 0.131

z= (112.57-112.8)/0.131 = -1.76

Will Power had the more convincing victory because his time was farther away from the mean in relation to Dario Franchitti.

m= 200

σ= 26

z= 1.5

x= 1.5*26+ 200 = 239

The minimum test score would be 239.

  1. 15% of these observations are less than or equal to 41.0 cm.

  2. 90% of waist circumferences of females 2 years of age are less than or equal to 52.7 cm.

  3. The 90th percentile of standing heights of males 20 years or older is less than or equal to 186.8.

    1. (x-xbar)/s

x=7.8

xbar= 10.08

s=

z score= (7.8-10.08)/s= (-2.28)/s

Q2- 9.95

Q1- 8.07

Q3- 11.83

  1. IQR= 3.76

  2. UF= 17.47

LF= 2.43

There are no outliers.

  1. The cutoff point (upper fence) is at 1463.4 minutes.

3.5

shape- right skewed

min= 0

Q1= 2

Q2= 3

Q3= 6

max= 16

shape- bell/symmetric

min= -1

Q1= 3

Q2= 5

Q3= 8

max= 11

  1. median= 40

  2. Q3= 54

  3. Y has more dispersion from the mean because the distance between Q1 and Q3 is larger.

  4. Variable x is symmetric because the box plot appears to be even on both sides and the whiskers are approximately the same length.

  5. Variable y is right skewed because the box plot has more data on the left side but has whiskers that extend farther away on the right side.

  1. median= 16

  2. Q1= 22

  3. Boxplot y has more dispersion because the distance between the two fences is larger than that of x.

  4. X has an outlier at data point 30.

  5. Y is left sloped because the data is not even on both sides. There is more data on the right hand side, but the whiskers on the left side extend farther away from the quartiles.

your_data <- c(60, 63, 68, 68, 68,
               75, 75, 77, 79, 89, 
               89, 89, 93, 94, 98)
             
boxplot(your_data, horizontal = T)

fivenum(your_data)
## [1] 60 68 77 89 98
this_data <- c(110, 125, 140, 140,140,
               150, 152, 157, 160, 173, 
               173, 173, 180, 180,205)
             
boxplot(this_data, horizontal = T)

fivenum(this_data)
## [1] 110 140 157 173 205
my_data <- c(42, 43, 46, 46, 47,
             47, 48, 49, 49, 50,
             50, 51, 51, 51, 51,
             52, 52, 54, 54, 54,
             54, 54, 55, 55, 55,
             55, 56, 56, 56, 57,
             57, 57, 57, 58, 60,
             61, 61, 61, 62, 64,
             64, 65, 68, 69)

fivenum(my_data)
## [1] 42.0 50.5 54.5 57.5 69.0
boxplot(my_data, horizontal = T)

Shape- The shape of this distribution appears to be symmetric/bell shaped.

our_data <- c(7.2, 7.8, 7.8, 7.9, 8.1, 8.3,
              8.5, 8.6, 8.6, 8.6, 8.7, 8.8,
              9.0, 9.1, 9.2, 9.2, 9.2, 9.4,
              9.4, 9.6, 9.7, 9.7, 9.9, 9.9,
              10.0, 10.0, 10.0, 10.1, 10.2,10.3,
              10.3, 10.3, 10.3, 10.7, 10.7, 10.9,
              11.2, 11.2, 11.2, 11.3, 11.3, 11.3,
              11.5, 11.5, 11.7, 12.4, 12.5, 13.6,
              13.8, 14.4, 16.4)


fivenum(our_data)
## [1]  7.20  9.05 10.00 11.20 16.40
boxplot(our_data, horizontal = T)

The shape of the distribution is slightly right skewed. This is because the right whisker seems to extend out further than the left whisker does. In addition to this, there is an outlier on the right side of this box plot at point 17.