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# Describing Distributions Homework

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?

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

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.

Stem-and-Leaf Plots in the Primary Grades
Continued

### Notes

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 StatisticsTM 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/.

### Solutions

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.