http://www.ck12.org Chapter 7. Organizing and Displaying Data
Guided Practice
The frequency polygon below represents the heights, in inches, of a group of professional basketball players. Use
the frequency polygon to answer the following questions:
a. How many players’ heights were measured?
b. What was the bin size of the histogram on which the frequency polygon is based?
c. What range of heights was most common among the basketball players?
d. What range of heights was least common among the basketball players?
e. What percentage of the basketball players measured had a height of less than 76.5 inches?
Answer:
a. To find the number of players whose heights were measured, just add up all of the frequencies. This can be done
as follows:
6 + 10 + 22 + 24 + 16 + 20 + 2 = 100
This means that 100 players’ heights were measured.
b. The bin size of the histogram on which the frequency polygon is based is 3. This is apparent from the fact that the
points that were connected to create the frequency polygon are 3 inches apart on the horizontal axis.
c. Remember that thex-coordinate of each of the points that were connected to create the frequency polygon is the
midpoint of one of the bins of the corresponding histogram. It’s obvious from the frequency polygon that 78 inches
has the greatest frequency, but this doesn’t necessarily mean that height most common among the basketball players
was 78 inches. All it means is that the range of heights that was most common among the basketball players was
76.5 inches to 79.5 inches.
d. For the same reason that the range of heights that was most common among the basketball players was 76.5
inches to 79.5 inches, the range of heights that was least common among the basketball players was 85.5 inches to
88.5 inches. Remember that the points at 66 inches and 90 inches along the horizontal axis were just added to give
the frequency polygon the appearance of having a starting point and an ending point.
e. The point at 75 inches along the horizontal axis represents the bin [73.5, 76.5). Therefore, to find the number
of basketball players measured who had a height of less than 76.5 inches, add the frequencies of the first 3 bins as