Learning Math: Data Analysis, Statistics, and Probability
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:
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.
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.
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.
Use the information from Problems H1-H3 to create a cumulative frequency and relative cumulative frequency chart for this data set.
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?”
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.
Reproduced with permission from Mathematics Teaching in the Middle School. Copyright © 1994 by the National Council of Teachers of Mathematics. All rights reserved.
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 Teaching Statistics <http://science.ntu.ac.uk/rsscse/ts/> and is used with permission.
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/.
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.
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.
Session 1 Statistics As Problem Solving
Consider statistics as a problem-solving process and examine its four components: asking questions, collecting appropriate data, analyzing the data, and interpreting the results. This session investigates the nature of data and its potential sources of variation. Variables, bias, and random sampling are introduced.
Session 2 Data Organization and Representation
Explore different ways of representing, analyzing, and interpreting data, including line plots, frequency tables, cumulative and relative frequency tables, and bar graphs. Learn how to use intervals to describe variation in data. Learn how to determine and understand the median.
Session 3 Describing Distributions
Continue learning about organizing and grouping data in different graphs and tables. Learn how to analyze and interpret variation in data by using stem and leaf plots and histograms. Learn about relative and cumulative frequency.
Session 4 Min, Max and the Five-Number Summary
Investigate various approaches for summarizing variation in data, and learn how dividing data into groups can help provide other types of answers to statistical questions. Understand numerical and graphic representations of the minimum, the maximum, the median, and quartiles. Learn how to create a box plot.
Session 5 Variation About the Mean
Explore the concept of the mean and how variation in data can be described relative to the mean. Concepts include fair and unfair allocations, and how to measure variation about the mean.
Session 6 Designing Experiments
Examine how to collect and compare data from observational and experimental studies, and learn how to set up your own experimental studies.
Session 7 Bivariate Data and Analysis
Analyze bivariate data and understand the concepts of association and co-variation between two quantitative variables. Explore scatter plots, the least squares line, and modeling linear relationships.
Session 8 Probability
Investigate some basic concepts of probability and the relationship between statistics and probability. Learn about random events, games of chance, mathematical and experimental probability, tree diagrams, and the binomial probability model.
Session 9 Random Sampling and Estimation
Learn how to select a random sample and use it to estimate characteristics of an entire population. Learn how to describe variation in estimates, and the effect of sample size on an estimate's accuracy.
Session 10 Classroom Case Studies, Grades K-2
Explore how the concepts developed in this course can be applied through a case study of a K-2 teacher, Ellen Sabanosh, a former course participant who has adapted her new knowledge to her classroom.
Session 11 Classroom Case Studies, Grades 3-5
Explore how the concepts developed in this course can be applied through case studies of a grade 3-5 teacher, Suzanne L'Esperance and grade 6-8 teacher, Paul Snowden, both former course participants who have adapted their new knowledge to their classrooms.