Make and interpret frequency tables and histograms.

You can organize data in a tally chart or a frequency table.  Another way to display the data is to use a histogram a special bar graph that represents the frequency of events.  There are no spaces between the bars of a histogram because there are no gaps between the intervals.

Different Ways to Display Frequency

Way 1:  You can use a frequency table.

Way 2:  You can use a histogram.

Practice

Use the histogram at left for Problems 1-6.

1.  How many riders are from 20 to 49 years old?

2.  How many of the riders are at least 40 years old?

3.  What's Wrong?  Lilith says there are more than 75 riders in the community bike rally.  Explain why she is wrong.

Adding

4.  Explain  Are most of the riders under 40 years of age?

5.  Analyze  Which bar of the histogram contains the median of the data?  How do you know?

6. Write About It  Redraw the histogram using four intervals instead of eight.  Which histogram gives more information?  Explain.

Use the histogram for Problems 7-10.

7.  How many more students saved $11-$20 each month than those who saved $0-$10?

8.  How many students are represented in the histogram?

9.  Which intervals have the same frequency?

10.  Which interval has the greatest frequency?

Answers

1.  38

2.  27

3.  Adding up the heights of all the bars, we see there are only 63 riders.

4.  Yes; 36 riders are under 40 years old, and this is more than half of the 63 total riders.

5.  The age 30-39 bar; with 63 riders, the median is the 32nd one when listed in order.  The first three bars contain a total of 20 riders, and the age 30-39 bar contains 16, so this is the bar that contains the 32nd rider.

6.  The eight-interval histogram gives more information because we can better see how the data is distributed among the age demographics.

7.  1

8.  26

9.  21-30 and 41-50

10.  31-40