3-StatKey Practice Part 2 ANSWERS-3

2 The dotplot looks almost flat, but it’s easy to miss the gaps. Looking at the histogram, though, takes away the effect of the gaps and shows that the distri- bution is right-skewed. (4) Now, let’s look at a different variable in the same dataset: DeathRate (you can switch to the new variable without uploading again using “Change Column(s)”). (a) Should we denote the mean using ¯ x or μ ? What is the mean? μ = 8 . 073 (b) Should we denote the standard deviation using s or σ ? What is the standard deviation? σ = 3 . 133 (c) Give the Five-Number Summary. 1, 5.95, 7.5, 9.7, 17.2 (d) Find the IQR. 9 . 7 - 5 . 95 = 3 . 75 (e) Compute the cutoffs for outliers using the 1 . 5 × IQR rule. 5 . 95 - 1 . 5 × 3 . 75 = 0 . 325 (low threshold;) 9 . 7+1 . 5 × 3 . 75 = 15 . 325 (high threshold) (f) Are there outliers? If so, what are they? All data values are above 0.325, so there are no low outliers. There are three values above 15.325: 15.4 (Dem. Rep. of Congo), 16.9 (Botswana), and 17.2 (Sierra Leone) are all high outliers. (g) What country has the highest death rate? What is its z -score? Sierra Leone; 17 . 2 - 8 . 073 3 . 133 = 2 . 913 (h) What countries have the lowest death rate? What are their z -scores? UAE; 1 - 8 . 073 3 . 133 = - 2 . 258 (i) Looking at the histogram, would you say the distribution is left-skewed, right- skewed, or symmetric? Which is more skewed, BirthRate or DeathRate ? DeathRate is also right skewed, but not as skewed as BirthRate . (j) The 95% Rule says that under certain circumstances, 95% of the data will fall within 2 standard deviations of the mean (put another way, 95% of the data will have z -scores between - 2 and 2). For which of these variables is that rule more likely to apply? Why? The 95% Rule applies to bell-shaped distributions; DeathRate is more bell- shaped, so the rule is more likely to apply to it. (k) How many birth rates fall more than 2 standard deviations away from the mean? What proportion is that? Repeat this question with death rates. mean – 2 SD mean + 2 SD below - 2 above +2 total proportion Birth rates 0.223 42.279 0 10 10 0.049505 Death rates 1.807 14.339 2 7 9 0.044335 Looks like the 95% rule applied pretty well to both in this case!