Homework #3 9/28/15

READING 3.4 QUESTIONS # 5-15 ODDS

5. Birth Weights: What is the z-score for a 34-week gestation period baby?

• -.303

What is the z-score for the 40-week gestation period baby?

• -.425

Which baby weighs less relative to the gestation period?

• The 40-week gestation baby weighs less because the z-score is less than that of the 34-week baby.

7. Men versus Women: Who is relatively taller, a 74-inch man or a 70-inch woman?

• A 75-inch man is relatively taller because his z-score is higher, at 1.8, than the woman’s at 1.55.

9. ERA Champions: Which player had the better year relative to his peers, Johnson or Hernandez? Why?

• Hernandez had the better year relatively because his z-score was -2.14, which is more standard deviations below the mean than Johnson, who’s z-score was -1.779.

11. IndyCar Races: Who had the more convincing victory?

• The Indy Grand Prix was more convincing because he finished more standard deviations below the mean, with a z-score of -1.756, compared to the Indy 500 which finished with a z-score of -1.476.

13. School Admissions: What is the minimum score that an applicant must make on the test to be accepted?

• 239

15. Explain the meaning of the following percentiles

1. 15% of males 3-5 months old are 41.0 cm or less.

2. 90% of 2-year-old females have a waist circumfrence equal to or less than 52.7 cm.

3. The 90th percentile represents 90% of men in that category, and in every age division, the 90th percentile decreased in value as age increased. Based on this information, it can be inferred that men are likely taller when they are in 20-29 years of age, and decrease in height slightly as they age.

READING 3.5 PROBLEMS #3-10

1. Identify the shape of the distribution

• Skewed right, because the median is left of center in the box, and the right whisker is longer than the left.

2. Determine the five-number summary

• The five number summary is (0, 1, 2.5, 6, 16)

1. Identify the shape of the distribution

• Symmetric, because the median is in the center of the box and left and right whiskers are roughly the same.

2. Determine the five number summary

• The five number summary is (-1, 2, 5, 8, 11)

5. Use the side-by-side boxplots shown to answer the quetions that follow.

1. To the nearest integer, what is the median of variable x?

• 40

2. To the nearest integer, what is the third quartile of variable y?

• 52

3. Which variable has more dispersion? Why?

• y has more dispersion because the maximum and minimun values are greater, so the spread is larger.

4. Describe the shape of the variable x. Support your position.

• The variable x is symmetric because the median is in the center of the box, so the distance from M to Q1 is the same as the distance from M to Q2, and the left and right whiskers are roughly the same length.

5. Describe the shape of the variable y. Support your position.

• The varible y is skewed right, because the median is left of center in the box, meaning that the distance from M to Q1 is less than the distance from M to Q3. Also, the right whisker is longer than the left.

6. Use the side-by-side boxplots to answer the questions that follow.

1. To the nearest integer, what is the median of variable x?

• 15

2. To the nearest integer, what is the first quartile of variable y?

• 10

3. Which variable has more dispersion? Why?

• y has more dispersion because the distance between the minimum and maximum value is greater, and therefore the spread is larger.

4. Does the variable x have any outliers? If so, what is the value of the outlier(s)?

• Yes, 30.

5. Describe the shape of the variable y. Support your position.

• The variable y is skewed left because the median is right of center in the box, meaning that the distance from the median to Q1 is more than the distance from M to Q3. In addition, the left whisker is longer than the right whisker.

7. Exam Scores: Draw a boxplot of the exam scores.

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

fivenum(your_data)

## [1] 60 68 77 89 98

8. Speed Reading: Draw a boxplot of the reading speed.

this_data <- c(110, 125, 140, 140,140,
               150, 152, 157, 160, 173, 
               173, 173, 180, 180,205)
             
boxplot(this_data, horizontal = T, col = c("palevioletred4"))

fivenum(this_data)

## [1] 110 140 157 173 205

9. Age at Inauguration

1. Find the five-number summary

• 42, 51, 54.5, 57, 69

2. Construct a boxplot

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, col = c("salmon"))

3. Comment on the shape of the distribution.

• The shape is skewed left, because the distance from the median to Q1 is more than the distance from the median to Q3.

10. Carpoolers

1. Find the five-number summary

• 7.2, 9.1, 10.0, 11.2, 16.4

2. Construct a boxplot.

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, col = c("plum1"))

3. Comment on the shape of the distribution.

• This boxplot is skewed right; the distance from M to Q1 is less than the distance from the distance from M to Q3. In addition, the right whisker is longer than the left.