Hw4_skeleton

3.4

• 1. Z-score
• 2. Kth percentile
• 3. Quartiles
• 4. Interquartile range
• 5. 34 week baby z score = -0.30 40 week baby z score = -0.43 The 40 week old baby weighs less relative to the gestation period
• 6. 34 week baby z score = 0.60 40 week baby z score = 0.85 The 34 week old baby weighs less relative to the gestation period
• 7. The 75-inch man is relatively taller because his z score is 1.8, while the 70-in womans z score is 1.55
• 8. The 62-in woman is relatively taller becuase her z score is -0.55, while the 67-inch mans z score is -0.87

1. A percentile rank of 5% means that 5% of 36 month old males weight is less than or equal to 12.0kg. So 95% of 36 month old males weigh more than 12.0kg

2. A percentile rank of 95% means that 95% of of newborn females height is less than or equal to 53.8 cm. So 5% of newborn females height is more than 53.8cm

1. Q1 = 25% of states have a violent crime rate that is 252.4 crimes/100,000 population or less. So 75% of the states have a violent crime rate greater than 252.4

Q2 = 50% of states have a violent crime rate that is 333.8 crimes/100,000 population or less. So 50% of the states have a violent crime rate greater than 333.8

Q3 = 75% of states have a violent crime rate that is 454.5 crimes/100,000 population or less. So 25% of states have a violent crime rate greater than 454.5

2. IQR = 202.1. This means that the range of the middle 50% of the observation have a range of 202.1 crimes/100,000 population

3. 1243.7 is above the upper fence (757.65), so the Washington DC crime rate is an outlier

4. The distribution is skewed right because the difference between Q2 and Q3 is greater than the difference between Q1 and Q2. The outier is also in the right tail, which implies it is skewed right

3.5

• 1. The minimun value in data set, Q1, the median (Q2), Q3 and the maximum value in the data set.
• 2. Skewed right

1. Skewed right

2. 5# Summary = 0, 1, 3, 6, 16

1. Symmetric

2. 5# summary = -1, 2, 5, 8, 11

1. Median of variable x = 40

2. Q3 of variable y = 52

3. Y has more dispersion because the range (whiskers) and the box are both much wider than that of variable x

4. Variable x is symmetric because the median is in the center of the box and the whiskers are the same length

5. Variable y is skewed right becuase the median is towards the left of the box and the right whisker is much longer than the left one

1. Median of variable x = 16

2. Q1 of variable y is 22

3. Variable y has more dispersion because the box is wider than the box of variable x, and variable y has longer whiskers

4. Variable x does have an outlier marked by the “*" to the right of the right whisker

5. Variable y is skewed left because the median is towards the right of the box and the left whisker is longer

data <- c(.608,.608,.608,.610,.612,
          .601,.610,.608,.607,.598,
          .606,.610,.605,.611,.600,
          .602,.607,.609,.608,.605,
          .611,.600,.605,.610,.603)

boxplot(data,horizontal = T)

2. Skewed left