Hw4_skeleton

3.4

• 1. The z score represents the number of standard deviations an observation is from the mean.
• 2. The kth percentile of a data set is a value such that K percent of the observations are less than or equal to the value.
• 3. Quartiles divide data into fourths.
• 4. Interquartile Range is the range of the middle 50% of the oberservations in the data set.
• 5. z score for 34 week gestation period baby=-.30 and z score for 40 week gestation period baby=-.43–this one is farthest from the mean so it weights less relative to the gestation period.
• 6. z score for 34 week gestation period baby=.61, z score for 40 week gestation period baby=.85–this one is farthest from the mean so it weighs less relative to gestation period
• 7. 75 inch man is relatively taller as z score of 1.8 is closer to the standard deviation
• 8. 62 inch woman is taller as the z score (-.55) is closer to the standard deviation of 3.8

1. A percentile rank of 5% means that 5% of 36 month old males have a weight less than or equal to 12 kg and 95% of 36 month old males weigh more than 12 kg

2. A percentile rank 95% means that 95% of newborn females have a length that is less than or equal to 53.8 cm and that 5% of newborn females have a length greater than 53.8 cm

1. Q1-25% of states have a crime rate of 252.4 per population of 100,000 while 75% of states have a crime rate greater than 252.4 in a population of 100,000. Q2-50% of states have a crime rate od 333.8 per population of 100,000 or less and 50% have a crime rate of 333.8 or more per population of 100,000. Q3-75% of states have a crime rate of 454.5 or less, while 25% have a crime rate of 454.4 or more

2. 454.5-252.4= 202.1, middle range of 50% of the oberservations is 202.1 crimes per population of 100,000

3. LF=252.4-1.5(202.1)=-50.75 UF=454.5+1.5(202.1)=757.65 Because the upper fence is this value, 12437 is an outlier

4. This is skewed right becuase the outlier is towards the right outside the upper fence and the difference between Q2 and Q3 (120.7) is larger than the difference between Q1 and Q2 (81)

3.5

• 1. Minimum, Q1, Median, Q3, Maximum
• 2. right

1. right skewed

2. 0,1,3,6,16

1. symmetric

2. -1,1,5,8,11

1. 40

2. 52

3. variable y has more dispersion as the whiskers are longer and the box itself is more spread out in length

4. data is symmetric, median at about the center, whiskers are about the same in length

5. Data is skewed right, median is to the left of center, right whisker is longer than the left

1. approx. 16

2. approx. 22

3. variable y. whiskers are longer, box itself is longer/more spread out

4. yes, approx. 29

5. left skewed, median is to the right of center, left whisker is far longer than the right

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. Because the median is to the right of the center and left whisker is longer than the right whisker, this box plot is skewed left.