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Numerade Educator

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Problem 14 Easy Difficulty

A National Vital Statistics Report (www.cdc.gov/nchs/) indicated that nearly 290,000 black Americans died in 2009, compared with just over 2 mil- lion white Americans. Here are histograms displaying the
distributions of their ages at death:
(FIGURE CAN'T COPY)
a) Describe the overall shapes of these distributions.
b) How do the distributions differ?
c) Look carefully at the bar definitions. Where do these plots violate the rules for statistical graphs?

Answer

a) When we look at histograms, we find that both histograms are unimodal and skewed to the
lower values. We can say that the distributions of ages at death of white and black Americans in
2009 are skewed to the left with possibly some outliers.
b) The typical age of death of white Americans is between 75 and 84 years while the typical age
of death of black Americans is between 65 and 74 years.
c) To construct a histogram, the class intervals should be continuous, that is, the upper boundary
of a class should be equal to the lower boundary of the next class. But in these plots, the class
intervals of ages are not continuous.

Discussion

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Video Transcript

Hi, Ron. So today we're gonna be looking at comparing these to Mr Grams. So that's part of question. I'm asked us to describe their poultry. I should mention that what these scrum show is the distractions off a use of death between white and black Americans. And so when we're asked to describe be able check, we could see that both these are, you know, metal. There's definitely only one sort of peak in both of these on that both pretty heavily left skewed or negatively skewed towards thes lower values. You know, you've got a real ramping book towards Hey, which is what we'd expect. You know, most people die with my older rather than when they were a child on. We might have some possible outliers. As we can see, you've got a little bumper not to fall in deaths of babies, which we wouldn't typically expect from this, because although we wouldn't know what to rule these out is out lies or not, without knowing the as with the deviation or the variance. So the books, like about this question, asks us, How did the restrictions differ? And so when we look at these, we could see that the typical age off death of white Americans is sort of in this 75 to plus really most death happened definitely in this very upper end. You know, 85 plus here. Whereas for black Americans, the debts here are shown to be typically around sort of 65 to 84. Yes, And so the, uh, the grass here assuring that the tickle age of death the black Americans is lower than the age of death of white Americans, the that question business about the that violation of rules. First, just photographs on what we can see here is that these are his grams. I'm you know, that history is have a look, it like effect, which essentially, if I do a quick diagram you have book. It's like this, and every value should full, no matter where they will fall into one of these buckets. And so what we should have is distinct boundaries. What? You have a very clear point where it falls and and so essentially, what I'm saying in a very long winded way is that we should have even and boundaries, you know, these should be continuous. So not 55 15 15 to 25. That shouldn't be this gap here in the middle on because this is representing a continuous, um, sort of variable. You know, people are 14.3, your 14.75 years old, and so, actually, if you're not exactly 14 years old or exactly 15 years old and there you would fall between this gap, I know that this doesn't necessarily make sense when you think of how you would consider measuring people ages. But when we construct distributions, it's really important that the history arms, especially this is a continuous instable.