Summary: This module is the complementary teacher's guide for the "Descriptive Statistics" chapter of the Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.
Graphs are important tools in statistics and probability. Graphs used in this course are the boxplot, the histogram, and the stem-plot. The histogram and boxplot are used extensively while the stem-plot is just demonstrated.
Discuss the measures of "center" - mean (average), median, mode. If you are using technology, it helps to show the students how to use technology to find the measures first. Then do some examples by hand. Distinguish between the symbols used for the sample mean and the population mean. Give an example where the mean is the best measure of the center and a second example where the median is the best example. (Example where median is the better measure: 19, 16, 46, 18, 21. Example where mean is the better measure: 18, 20, 23, 25, 25.) At the end of the chapter, there is a summary of the mean formulas if you desire to go over them.
Discuss the measures of spread - variance and standard deviation. Stress that the standard deviation is the square root of the variance. Differentiate between the sample and population standard deviations. Dividing by
Discuss the measures of location - quartile and percentile. For many students, these measures are difficult. It is better to make up a relative frequency table from an example like the one in the book (the amount of sleep 50 students get per school night) and find quartiles and percentiles. Graphing calculators typically calculate quartiles.
We introduce the formula
Have students work in groups to complete Practice 1 and Practice 2.
If you are using the TI-83 or TI-84 calculator series, go over the calculator instructions in the text for entering data and calculating the sample mean, the sample standard deviation, the quartiles, constructing histograms, and construction boxplots. The calculator instructions can also be found on the Texas Instruments website and the appropriate Guidebook.
Assign Homework. Suggested problems: 1 - 23 odds, 24 - 30.