3.4

  1. z-score for 34-week baby: - 0.303 z-score for 40-week baby: - 0.426 the 40 week baby weighs less relative to the gestation period because it has a further standard deviation away from the mean.

  2. The man has a z-score of 1.8, while the woman has a z-score of 1.6. Because the z-score of the man is higher, he is relatively taller.

  3. While both players had z-scores below the mean, Hernandez did better relative to his peers as his z-score was -1.913, while Kershaw had a z-score of -2.302. So, Hernandez’s score was closer to the mean (average of his peers), so he did relatively better.

  4. Ryan is better in the 100 meter race because his z-score is closer to the mean than his z-score in the 200 meter race.

  5. The minimum score that an applicant must make on the test is 239 in order to be accepted.

  1. 85% of males 3-5 years old have a head circumference of 41.0 cm

  2. 10% of females that are 2 years old have a waist circumference of 52.7 cm.

  3. 90% of men ages 20 or older tend to be on the lowest end of the heigh spectrum, while 10% tend to be on the highest end. Thus, it is more common to be to have a smaller standing height than a larger one. Also, the older the man gets, the smaller his standing height, no matter what percentile (though the previous observation still applies).

22

  1. (hint the mean = 10.08, standard deviation = 1.885), z-score= 2.453. So Blackie’s hemoglobin count is 2.453 standard deviations above the averga of the hemoglobin count in the sample of cats.

  2. Q1= 9.15; Q2= 9.95; Q3= 11.1

  3. IQR= 1.95– not a large IQR, which suggests a low standard deviation as well.

  4. Lower Fence= 6.225 Upper Fence= 14.025 Lower outliers: 5.7 Upper outliers: n/a

  1. The upperfence (cut-off point) is 574.25 minutes.

3.5

3

  1. right-skewed

  2. min: 0; Q1: 2; median: 3; Q3: 6; Max: 16

4

  1. bell-shape

  2. min: -1; Q1: 2; median: 5; Q3: 8; max: 11

5

  1. 40

  2. 52

  3. Variable Y has more dispersion because it has a larger range which causes it to have a larger dispersion.

  4. Variable X is bell-shaped as it has no skew, but it is a skinner bell curve as it has a small but evenly spaced range.

  5. Variable Y is right-skewed, as it’s tail stretches out more so to the right, but it’s quartiles are all pushed together towards the left. So it has some data points that pull the whisker further to the right, but most of the points are left-wards.

6

  1. 16

  2. 22

  3. Variable Y has more dispersion because it has a larger range.

  4. Yes, the outlier is 29.

  5. Variable Y is skewed left as the left whisker of the boxplot extends further than the right whisker. Also, all the quartiles are pushed to the right, suggesting most of the data points are higher on the number line but that there are some points that drag the left whisker, making it skewed.

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. min: 42; Q1: 50; Q2: 54; Q3: 57; max: 69

boxplot(dat3)

  1. slight right-skew but mostly bell-shaped

10

dat3 <- c(7.2, 7.8, 7.8, 7.9, 8.1, 8.3,
          8.5, 8.6, 8.6, 8.6, 8.7, 8.8,
          9.0, 9.1, 9.2, 9.2, 9.2, 9.4,
          9.4, 9.6, 9.7, 9.7, 9.9, 9.9,
          10.0, 10.0, 10.0, 10.1, 10.2, 10.3,
          10.0, 10.3, 10.3, 10.7, 10.7, 10.9,
          11.2, 11.2, 11.2, 11.3, 11.3, 11.3,
          11.5, 11.5, 11.7, 12.4, 12.5, 13.6,
          13.8, 14.4, 16.4)

  1. min: 7.2; Q1: 8.9; Q2: 9.95; Q3: 10.55; 16.4

boxplot(dat3)

  1. definitely skewed right- the dispersion creates a much longer right whisker for the box plot than left whisker. The quartiles are all very close in terms of deviation to each other, and much closer to the minimum value than to the maximum value.