Hw4_skeleton

3.4

• 1. z-score
• 2. kth percentile, denoted Pk
• 3. quartiles
• 4. interquartile range
• 5. (2400-2600)/660 = -0.30 -> 34 week gestation, (3300-3500)/470 = -0.43 -> 40 week gestation. The 40 week baby weighs less relative to the gestation period.
• 6. (3000-2600)/660 = 0.61 -> 34 week gestation, (3900-3500)/470 = 0.85 -> 40 week gestation. The 34 week baby weighs less relative to the gestation period.
• 7. (75-69.6)/3.0 = 1.8 -> 75 inch man, (70-64.1)/3.8 = 1.55 -> 70 inch woman. The 75 inch man is relatively taller than the 70 inch woman.
• 8. (67-69.6)/3.0 = -0.87 -> 67 inch man, (62-64.1)/3.8 = -0.55 -> 62 inch woman. The 62 inch woman is relatively taller than the 67 inch man.

1. 5% of males aged 36 months of age weigh 12kg or less.

2. 95% of females are born at the length of 53.8cm or less while 5% are born at a greater length than 53.8cm.

1. 25% of the states have a crime rate of 252.4 crimes per 100,000 people or less whilst 75% have a crime rate higher than 252.4. 50% of the states have a crime rate that is 333.8 per 100,000 or less people whilst the other 50% has a crime rate greater than 333.8. 75% of the states have a crime rate of 454.5 per 100,000 people or less whilst 25% have a crime rate higher than 454.5.

2. 454.5-252.4 = 202.1. The middles 50% of all observations have a range of 202.1 crimes per 100,000 population.

3. LF = 252.4 - 1.5(202.1) = -50.75, UF = 454.5 + 1.5(202.1) = 757.65. 1459 is greater than the upper fence, therefore the crimerate in Washington, D.C. is an outlier.

4. Skewed right. This is because the difference between Q1 and Q2 is less than the difference between Q2 and Q3 and the outlier is also in the right tail of the distribution, implying that the distribution is skewed right.

3.5

• 1. The 5 number summary consists of the minimum value in the data set, the first quartile, the median, the third quartile and the maximum value in the set.
• 2. Right

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

2. The summary is, 0, 1, 3, 6, 16

1. Symmetric

2. The summary is, -1, 2, 5, 8, 11

1. For the variable x: M = 40

2. For the variable y: Q3 = 52

3. Y has more dispersion. This can be seen by the broader range and the much broader interquartile range.

4. The distribution of the variable x is symmetric. This can be seen because the median is 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 line.

1. For the variable x: M = 16

2. For the variable y: Q1 = 22

3. Y has more dispersion. This can be seen by the broader range and the much broader interquartile range.

4. Variable x has an outlier. The value is approximately 29.

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

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