3.4

5 The 34 week old baby has a weight that is .30 standard deviation below the mean and the 40 week old baby has a weight that is .43 below the mean. Therefore, the 40 week old baby weighs less in comparison to the gestation period.

7 The height of the 75in man is 1.8 standard deviations higher then the mean while the 70in woman’s height is 1.55 standard deviations higher then the mean. Therefore, the 75in man is taller with respect to the woman.

9 Felix’s ERA is 1.91 standard deviations below the mean while Clayton’s ERA is 2.3 standard deviations below the mean. Therefore, Clayton’s ERA is better relative to his peers because it is lower.

11 Ryan’s 100 meter back stroke has a standard deviation of 3.39 below the mean and his 200 meter back stroke has a standard deviation of 3.05 below the mean. Therefore, hia 100 meter back stroke is better because it is higher.

13 The minimum score that an applicant must make on the test to be accepted is a 239.

15

  1. The 15th percentile of the head circumference of males 3 to 5 months of age have a circumference that is equal to or less then 41 cm.

  2. The 90th percentile of the waist circumference of females 2 years of age is equal to or less than 52.7cm.

  3. The higher the percentile, the higher the height and the lower the percentile, the lower the height.

22

  1. The z score corresponding with Blackie is 1.24.

  2. Quartile 1 = 9.15 Quartile 2 = 9.95 Quartile 3 = 11.1

  3. The IQR for this data is 1.95.

  4. Lower fence = 7.2 Upper fence = 14.025

25 The cutoff point is 574.25.

3.5

3

  1. The distribution is skewed right because the right line is longer then the left and quartile 2 or the median lies slightly to the left.

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

4

  1. The distribution is symmetric because it is equally dispersed on both sides.

  2. The five number summary is -1, 3, 5, 8, 12.

5

  1. The median for x is 40.

  2. Quartile 3 = 52 for the variable y.

  3. Variable y has greater dispersion because it has a larger range and is more spread out.

  4. The distribution for x is symmetric because the median lies in the center and the data is equally dispersed.

  5. Variable y is skewed right because the right line is longer then the left and the median is towards the left.

6

  1. The median for x is 16.

  2. Quartile 1 is 23.

  3. Y has a greater dispersion because its range is larger.

  4. Yes, there is an outlier in x. The outlier is 30.

  5. The variable y is skewed left because the line on the left is much longer and quartile 2 or the median lies further to the right.

7

dat1 <- c(60,68,77,89,98)

boxplot(dat1)

8

dat2 <- c(110,140,157,173,205)

boxplot(dat2)

9

dat3 <- 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)

  1. The five number summary is 42, 50.5, 54.5, 57.5, 69.

boxplot(dat3)

  1. The shape of the distribution is symmetric because the median lies at the center.