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This series of problems leads you through the creation of a histogram and its corresponding tables for the data in Parts B and C, which you will now group by fives. Start with the stem and leaf plot for the grouping-by-fives scenario:

**Problem H1
**Create a grouped frequency table for this data set where the intervals have a width of five seconds.

The first interval will be 30 to < 35, the next will be 35 to < 40, etc. The last interval will be 90 to < 95.

**Problem H2
**Create a histogram for this data set where the intervals have a width of five seconds.

If you have difficulty, refer to the guide in Part B.

**Problem H3
**Using either the histogram or the grouped frequency table, create a relative frequency table and relative frequency histogram for this data set.

Refer to the guide in Part C if you have trouble here.

**Problem H4
**Use the information from Problems H1-H3 to create a cumulative frequency and relative cumulative frequency chart for this data set.

**Problem H5
**Using only the histogram and grouped relative frequency table based on an interval width of five, give two descriptive statements that provide an answer to the question “How well do people judge when a minute has elapsed?”

**Problem H6
**Based on the information in these problems, is it now possible to go back and answer any of the questions in Problem C1 that previously could not be answered with a histogram? Can you give more accurate answers for some of the questions in Problem C1? Are there some questions that still cannot be answered with a histogram?

**Suggested Readings:**

**Kader, Gary and Perry, Mike (September-October, 1994). Learning Statistics with Technology. Mathematics Teaching in the Middle School, 1 (2), 130-136.**

Reproduced with permission from

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Learning Statistics with Technology

Continued

Continued

**Pereira-Mendoza, Lionel and Dunkels, Andrejs (Summer, 1989). Stem-and-Leaf Plots in the Primary Grades. Teaching Statistics, 11 (2), 34-37. **

This article first appeared in

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Stem-and-Leaf Plots in the Primary Grades

Continued

**Note 5
**If you are working in a group, use your own data for the Ordering Hats activity. Each person should measure the head circumferences of several adults ahead of time, then bring their data to class. The group should have a total of 50-60 head circumferences for their data set. Also, consider having each person measure an equal number of men’s and women’s head circumferences. As an extension, you can look at the data separately for each sex.

Fathom Dynamic Statistics^{TM} Software, used by the onscreen participants, is helpful in creating graphical representations of data. You can use Fathom software to complete Problems D3-D13, as well as Homework Problems H1-H6. For more information, go to the Key Curriculum Press Web site at http://www.keypress.com/fathom/.

**Problem H1**

**Problem H2
**

**Problem H3
**

**Problem H4
**

**Problem H5**

All of the response times are between 30 and <95 seconds. There is a concentration of responses (42 of 52) between 50 and < 80 seconds. The most frequently occurring interval is from 55 to < 60 seconds, followed by both 60 to < 65 seconds and 65 to < 70 seconds.

**Problem H6
**Yes, questions (g) and (h) can now be answered, since the intervals are broken up by fives. The only question that still cannot be answered is (i), the percentage of responses that are equal to 60 seconds.