1. MTH 232 Section 13.1 Organizing and Representing Data

2. Key Ideas Statistics is a way to organize, present, and represent data through a variety of methods. The various numerical definitions of the center (mean, median, and mode) or a set give different insights into which measure of the center of the data is most revealing. Prior to the middle grades, students should have had experiences collecting, organizing, and representing sets of data.

3. Dot Plots Used to summarize relatively small sets of data. Dots are placed above the number line. At a glance, certain information—range of scores, where most scores are located, what the “typical” score is, which scores are atypical, or outliers.

4. Example Test scores from a recent MTH 100 test: 90, 73, 78, 80, 64, 48, 58, 61, 88, 49, 39, 49, 48, 80, 55, 84, 53, 64, 78, 82, 58, 76, 51, 54, 52, 15, 89

5. Stem-and-Leaf Plots Similar to dot plots Especially useful for comparing two sets of data. One part of the data value is the “stem” and the other part is the “leaf” Data must first be grouped by the “stem”, them ordered by the “leaf”

6. Another Example Another set of MTH 100 test scores: 46, 56, 71, 96, 46, 72, 88, 97, 70, 78, 84, 92, 86, 97, 73, 45, 41, 85

7. Histograms Scored are grouped into intervals. The height of the rectangle constructed on an interval indicates the number of data points in that interval (frequency). In a histogram, detail about the data is exchanged for the ability to visualize larger sets of data.

8. Line Graphs Especially useful for showing changes in data over time. Average Temperature in Tuscaloosa, Alabama MonthTempMonthTemp Jan48Jul80 Feb48Aug81 Mar58Sep75 Apr64Oct63 May71Nov53 Jun79Dec48

9. Bar Graphs Similar to histograms, but the horizontal axis contains categorical (non-numeric) data. The height of the bar indicates the frequency of the particular category. Random Question: which color of M&M’s is most occurring in a bag?

10. The answer may surprise you…