Hw4_skeleton

3.4

• 1. z-score
• 2. kth percentiles
• 3. quartiles
• 4. the interquartile range
• 5. z score of 34 week gestation = -0.30. z score of 40 week gestation = -0.43. The 40-week gestation baby weighs less relative to the gestation period.
• 6. z score of 34 week gestation = 0.61 (rounded). z score of 40 week gestation =.85. The 34-week gestation period baby is .61 standard deviations above the mean while the 40-week gestation period baby is .85 standard deviations above the mean. Thus, the 34 week gestation baby weighs less relative to gestation period.
• 7. 75 inch man: 75-69.6/3 = 1.8 70 inch woman: 70-64.1/3.8 = 1.55 (rounded)

  The height of the 75-inch man is 1.8 standard deviations above the mean, while the height of a 70-inch woman is 1.55 standard deviations above the mean. Thus, the 75-inch man is relatively taller than the 70 inch woman.

• 8. 67 inch man: 67-69.6/3 = -0.87 (rounded) 62 inch woman: 62-64.1/3.8= -0.55 (rounded)

  The height of the 67 inch man is .87 standard deviations below the mean. The height of the 62 inch woman is .55 standard deviations below the mean. Thus, the 62 inch woman is relatively taller.

1. This means that 95% of the total of 36 months of age males weigh more than 12.0kg, and 5% of the total weigh less than 12.0kg.

2. This means that 95% of all newborn females have a length less than 53.8cm, and 10% of all newborn females have a length longer than 53.8cm.

1. 25% of the states have a violent crime rate that is 252.4 crimes per 100,000 population or less, and 75% (100-25)% of the states have a violent crime rate more than 252.4. 50% of the states have a violent crime rate that is 333.8 crimes per 100,000 population or less, while (100-50)% = 50% of the states have a voilent crime rate more than 338.8. 75% if the states have a violent crime rate that is 454.5 crimes per 100,000 population or less, and (100-75)% = 25% of the states have a violent crime rate more than 454.5.

2. IQR = 454.5-252.4= 202.1 crimes per 100,000 population. This means the middle 50% of all observations have a range of 241.0 crimes per 100,000 population.

3. Lower Fence: 252.4 - 1.5(202.1) = -50.75 Upper Fence: 454.5 + 1.5(202.1) = 757.65 Since, 1,459 is above the upper fence, the Washington DC crime rate is an outlier

4. I believe that it is skewed right. The difference between q1 and q2 (81) is less thant he difference between q2 and q3 (120.7), and the outlier is in the right tail of the distribution, which would suggest it be skewed to the right.

3.5

• 1. The five number summary consitsts of the minimum value in the date set, the first quartile, the median, the third quartile, and the maximum value in the date set.
• 2. right

1. the median is to the left of the center of the box and the right line is substantially longer than the left line, so the distribution is skewed right.

2. reading the boxplot, the five-number summary is: 0, 1, 3, 6,

a)the median is at or near the center of the box, and the whiskers are of equal lengths, so the distribution is symmetric.

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

1. For the variable x: M = 40

2. For the variable y: Q3 = 52

3. The variable y has more dispersion, which can be seen by the broader range, AKA the span of the lines, and the much broader IQR (span of the box).

4. The distribution of the variable x is symmettric, which can be seen due to the median being near the center of the box and the horizontal lines are approximately the same in length.

5. The distribution of the variable y is skewed right. This can be seen because the median is to the left of the center of the box and the right line is substantially longer than the left.

1. For the variable x: M=16

2. For the variable y: q1=22

3. The variable y has slightly more dispersion, which can be seen by the broader range, AKA the span of the lines, and the much broader IQR (span of the box).

4. Yes variable x does have an outlier valued at 29.

5. The shape of variable y is skewed left, which can be seen because the median is to the right of the center of the box, and the left whisker is longer than the right one.

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. The shape of variable y is skewed left, which can be seen because the median is to the right of the center of the box, and the left whisker is longer than the right one.