1. MAT 157: Stats I Ch 1 and 2

2. What is Statistics? The art and science of collecting, analyzing, presenting, and interpreting data The art and science of collecting, analyzing, presenting, and interpreting data -Larose, pg 7 -Larose, pg 7 “art”—judgment, experience, and intuition are tools “art”—judgment, experience, and intuition are tools Phase 1: Data Collection Phase 1: Data Collection Phase 2: Data Analysis Phase 2: Data Analysis Phase 3: Data Presentation Phase 3: Data Presentation Phase 4: Data Interpretation Phase 4: Data Interpretation

3. Statistics Basics Population-ALL individuals/items under consideration Population-ALL individuals/items under consideration Sample-the part of the population from which information is collected Sample-the part of the population from which information is collected

4. Classify a study as… Inferential statistics-uses a sample to make conclusions/prediction about the population Inferential statistics-uses a sample to make conclusions/prediction about the population Descriptive statistics-an organization and summarization of information (just states raw data) Descriptive statistics-an organization and summarization of information (just states raw data)AND Observational Study-researcher only observes (reveals associations) Observational Study-researcher only observes (reveals associations) Designed Experiment-researcher imposes treatments and controls (reveals causations) Designed Experiment-researcher imposes treatments and controls (reveals causations)

5. Gathering Information Census Census Sampling Sampling Experimentation Experimentation Simple Random Sampling-process in which all are equally likely to be part of the sample. Simple Random Sampling-process in which all are equally likely to be part of the sample. –with replacement and without replacement Simple Random Sample-the sample obtained from using simple random sampling. Simple Random Sample-the sample obtained from using simple random sampling.

6. Table of Random Numbers

7. Other Ways to Get Simple Random Samples? Would these give a representative sample?

8. Organizing Data Variable Variable –Quantitative…numerical variable  Discrete  Continuous –Qualitative…nonnumeric variable (also called categorical variables)

9. Organizing Data (cont) Data-values of the variable Data-values of the variable –Quantitative data  Discrete  Continuous –Qualitative data –Ordinal data…data about order or rank

10. Organize QUALITATIVE data Frequency distribution Frequency distribution Relative-frequency distribution Relative-frequency distribution Pie Chart Pie Chart –Select the information you want in the chart first. Bar Chart (bar graph) Bar Chart (bar graph) Data Lab Data Lab  Excel Collegefrequency IOWA8 ISU5 UNI3 16 Relative frequency 0.5000 0.3125 0.1875 1.0000 Grouped Data Table

11. General Excel ™ Process Select the information you want in your graph or chart. Include your headings (but not any totals) Select the information you want in your graph or chart. Include your headings (but not any totals) Insert the chart Insert the chart –If the axis didn’t end up right, select the axis on the chart and right click – Choose “select data…” –Chose “edit the (horizontal or vertical) axis label” – then select the values from your spreadsheet that should be the horizontal axis. Select OK

12. Excel ™ Process Extras To change the gap & color To change the gap & color –Cursor over a bar, right click –Select “Format Data Series…” –Go to the “Series Options” tab (to the left) –Change the “Gap Width” to No Gap –Go to the “Fill” tab (to the left) –Select the type of fill/color you want –Go to the “Border Color” tab (to the left) –Select the type/color of border you want (make the border a different color than the fill)

13. Organizing Quantitative Data Grouping Single value grouping Single value grouping Limit grouping Limit grouping –Lower limit (smallest that can go in a class) –Upper limit (largest that can go in a class) –Class width (difference of the lower limit & the lower limit of the next class) –Class mark (average of the two class limits of a class) Cutpoint grouping Cutpoint grouping –lower cutpoint –Upper cutpoint ( the smallest value that goes into the next higher class) –Class width (difference between the cutpoints) –Class midpoint (average of the two cutpoints)

14. Options for Organizing Quantitative Data Frequency Distribution Frequency Distribution Relative Frequency Distribution Relative Frequency Distribution Grouped Data Table Grouped Data Table Histogram Histogram Dot Plot Dot Plot Stem and Leaf Stem and Leaf

15. Histogram- Quantitative Data Similar to a bar graph, but the x-axis is usually a range of values (if it is single value grouping, the single value would go in the middle of the bar) Similar to a bar graph, but the x-axis is usually a range of values (if it is single value grouping, the single value would go in the middle of the bar) Some title?? FrEquencyFrEquency

16. Other ways to organize quantitative data Dotplots Dotplots 210, 219, 218, 225, 223, 250, 210, 219, 218, 225, 223, 250, 258, 238, 199, 218, 213, 213 258, 238, 199, 218, 213, 213 Stem-and-Leaf Diagrams Stem-and-Leaf Diagrams 210, 219, 218, 225, 223, 250, 258, 238, 199, 218, 213, 213 258, 238, 199, 218, 213, 213

17. Distribution Shapes The distribution of a data set is a table, graph, or formula that provides the values of the observations and how often they occur. The distribution of a data set is a table, graph, or formula that provides the values of the observations and how often they occur. Skewed: Visual of shapes (book pg 63, 64) Skewed: Visual of shapes (book pg 63, 64)

18. Population and Sample Distributions Population data/distribution vs sample data/distribution Population data/distribution vs sample data/distribution For simple random sampling, the sample distribution approximates the population distribution (the bigger the sample the better the approximation) For simple random sampling, the sample distribution approximates the population distribution (the bigger the sample the better the approximation)

19. Misleading Graphs http://businessofsoftware.org/2007/09/start-a-softwar/

20. Why misleading? http://googlediffable.blogspot.com/2010/07/mea-culpa-on-performance-graph.html

21. Why misleading? http://www.narragansett.k12.ri.us/resources/necap%20support/gle_support/Math/resources_data/ident_rep_ele m.htm

22. Misleading? http://where-inspiration-happens.blogspot.com/2010/11/week-11-information-graphics-who-says.html

23. Misleading Graphs Truncated Graphs Truncated Graphs Improper Scaling Improper Scaling http://simplystatistics.org/2012/11/26/the- statisticians-at-fox-news-use-classic-and- novel-graphical-techniques-to-lead-with-data/ http://simplystatistics.org/2012/11/26/the- statisticians-at-fox-news-use-classic-and- novel-graphical-techniques-to-lead-with-data/ http://simplystatistics.org/2012/11/26/the- statisticians-at-fox-news-use-classic-and- novel-graphical-techniques-to-lead-with-data/ http://simplystatistics.org/2012/11/26/the- statisticians-at-fox-news-use-classic-and- novel-graphical-techniques-to-lead-with-data/

24. Review Vocabulary Vocabulary –Statistics –Population vs Sample –Inferential vs Descriptive –Observational vs Designed Experiment –Census, sampling, experimentation –Simple Random Sample –Quantitative vs Qualitative vs Ordinal –Discrete vs Continuous –Frequency vs Relative Frequency Organizing Qualitative Data Organizing Qualitative Data –Frequency –Relative Frequency –Grouped data table –Pie chart –Bar chart Organize Quantitative Data Organize Quantitative Data –Frequency –Relative Frequency –Grouped Data Table –Dot Plot –Stem and Leaf –Histogram