What is important to a statistician is that the second bar graph is better than the
first. It is better because it provides us with a more accurate depiction of reality,
because we have taken into account a larger population. Another way to say this
is that the second bar graph has a smaller margin of error. The SAT might test
your understanding of this in the following way:
A statistician is trying to determine the average time a high school
swimmer can hold his breath underwater, so she asks 30 high school
swimmers how many seconds they can hold their breath underwater.
The mean (average) response is 55 seconds, with a margin of error of
10 seconds. Another statistician wants to replicate the study, but with a
smaller margin of error. Which of the following would accomplish
this:
A) Ask 15 high school swimmers
B) Ask 300 randomly selected people
C) Ask 300 high school swimmers
D) Ask 15 randomly selected peopleRemember that a larger population size decreases our margin of error, so A
and D are out. The initial study focused on high school swimmers, so answer
choice B expands the population too widely. Our correct answer choice, then, is
C.
The last tricky element of statistics is determining exactly which conclusions
can and cannot be drawn from a set of data. Let’s go back to the bar graph about
American student test scores on the previous page. The SAT might throw this
particularly devious question at you:
Which of the following can best be inferred from the graph:
A) It is easiest to achieve a score in the 1000–1400 range.
B) Our education system does not prepare students adequately to
achieve a score above 1400.
C) Any student is most likely to score in the 1000–1400 range.
D) Any student in America is most likely to score in the 1000–1400
range.The problem with answer choice A is that the graph only records scores, not the
ease with which those scores were attained. B might very well be true, but the