Read histograms and frequency polygons.
A company that makes vitamins is sponsoring a program on a cable TV channel. The
marketing department must choose from three advertisements to show during the
program.
1.Children talking about a chewable vitamin that the company makes.
2.A college student talking about an active-life vitamin that the company makes.
3.A grandmother talking about a multivitamin that the company makes.
A survey of the viewing audience records the age of each viewer,
counting the number in the 6-to-15-year-old age group, the 16-to-
25-year-old age group, and so on. The graph of the data is displayed in
a special type of bar graph called a histogram,as shown on the right.
The vertical axis, labeled Frequency,indicates the number of viewers
in each age group. For example, the histogram shows that 105 viewers
are in the 36-to-45-year-old age group.
A histogram is a bar graph with three important features.
1.The bars of a histogram touch.
2.Data values never fall at the edge of a bar.
3.The widths of each bar are equal and represent a range of values.
The width of each bar of a histogram represents a range of numbers called a class
interval.The histogram above has 7 class intervals, each representing an age span of
10 years. Since most viewers are in the 16-to-25-year-old age group, the marketing
department decides to advertise the active-life vitamins in commercials that appeal to
young adults.
67.1 Reading Graphs and Tables 601505.5 15.5 25.5 35.5
Age45.5 55.5 65.5 75.5100150200Frequency250Age of Viewers of a Cable TV Channel75230160
105(^3714)
10
EXAMPLE (^8) Carry-on Luggage An airline weighed the carry-on
luggage of 2,260 passengers. The data is displayed in the histogram below.
a.How many passengers carried
luggage in the 8-to-11-pound
range?
b.How many carried luggage in
the 12-to-19-pound range?
StrategyWe will examine the
scale on the horizontal axis of the
histogram and identify the interval
that contains the given range of
weight for the carry-on luggage.
WHYThen we can read the height
of the corresponding bar to answer
the question.
Solution
a.The second bar, with edges at 7.5 and 11.5 pounds, corresponds to the 8-to-11-
pound range. Use the height of the bar (or the number written there) to
determine that 430 passengers carried such luggage.
b.The 12-to-19-pound range is covered by two bars. The total number of
passengers with luggage in this range is 970 540, or 1,510.
Self Check 8
CARRY-ON LUGGAGERefer to the
histogram of Example 8. How
many passengers carried luggage
in the 20-to-23-pound range?
Now TryProblem 61
Weight of Carry-on Luggage
100
3.5 7.5 11.5 15.5
Weight (lb)
19.5 23.5
300
500
700
Frequency
900
1,100
120
430
970
540
200
c. At any time, the height of a line gives the distance a train has traveled. Both trains
have traveled the same distance whenever the two lines are the same height—
that is, at any time when the lines intersect. This occurs at times C and E.