Answers to Sample Questions
A. What percentage of people scored 70 or over on this test?
Answer: 98 percent.
Solution: The area of the rectangle above the interval 50-to-70 is about width*height = 0.001*20 = .02 so all but 2 percent of the area under the histogram is over the interval 70-to-150.
B. Which interval is more crowded: 90-100 or 100-110?
Answer: 100-110.
Solution: The density is greatest over the interval 100-110 so this is the most crowded interval.
C. In which interval are there more test scores: 120-130 or 130-150?
Answer: 120-130
Solution: There are more scores in the interval which has the larger rectangle. The area of the rectangle over the interval 120-130 is larger because its area is about width*height = 0.006*10 = .06 and the rectangle over the interval 130-150 is about .0008*20=.016.
D. What is the 50th percentile?
Answer: The median is just short of 100.
Solution: The median is the 50th percentile. A vertical line at a score just a little less than 100 splits the area of the histogram into two equal parts.