1. Chapter 2 - Descriptive Statistics Goal: To organize and describe data sets to make the data easier to understand. Frequency Distributions and their graphs. Stem-and-Leaf Plots Dot Plot Pie Chart Measures of Central Tendency Measures of Variation Measures of Position The Shape of Frequency Distributions

2. Frequency Distributions A frequency distribution is a table that shows classes of data entries with a count of the number of entries in each class (called the frequency). Each class has a lower limit (the smallest number that can belong to a class) And an upper limit (the biggest number that can belong to a class. The class width is the distance between the lower limits of consecutive classes. Range = largest data entry – smallest data entry.

3. Constructing Frequency Distributions 1. Decide how many classes you want (5-20). 2. Determine Class width: Class width = Range/Number of Classes (Rounding should be consistent with data) 3. Find the class limits. Use the smallest data entry as the lower limit of the first class. Add class width to lower limit to get lower limit of the next class. Remember: Classes cannot overlap. 4. Determine the frequency for each class.

4. Dollars Spent on Books for a Semester 91376142266190 472188273248398 279341189101188 249266130375269 53019948948643 30 1273548498

5. Graphs of Frequency Distributions A histogram is a bar graph of a frequency distribution. Properties: Data is quantitative Consecutive bars must touch Horizontal scale measures data values Vertical scale measures class frequency

6. Graphing Quantitative Data Sets: Stem-and-Leaf Plots and Dot Plots Dollars Spent on Books 30127189266341472 43130190266354486 84142199269375489 91188248273376530 10118824927939898

7. Graphing Qualitative Data: Pie Charts Major Psychology-BA Justice Studies- BA/Sociology-BAContinuing EducationSE Mathematics-IM Biology - BA/Clinical Lab Sciences-BSNursingUndergraduate UndeclaredPolitical Science-BA Psychology-BANursing ELED Gen Cont Mathematics-BANursing Sociology-BA/Management (General)-Minor Modern Languages: SpanishSociology-BA Justice Studies- BA/Sociology-BA Computer Science- BS/Music-MinorArt Studio-BFA SE English-IM Nursing

8. Last Time: Let's devise an experiment to see if for commercially available chocolate chip cookies price translates into quality. Devise an experiment to answer this question. Work in small groups to come up with a plan for the experiment. Generate your ideas for a good experiment with as much detail as possible.

9. Pareto Chart Bar chart used to display qualitative Data Properties: Bars do not touch Bars are positioned in decreasing order

10. Graphing Paired Data Sets Number of Students per teacherAverage teacher’s salary (in thousands of dollars) 17.128.7 17.547.5 18.931.8 17.128.1 20.040.3 18.633.8 14.449.8 16.537.5 13.342.5 18.431.9

11. Mexican Lemons Have Improved Highway Safety Global Warming has Pirates on the Rise Correlation vs Causation

12. Time Series Data A data set that is composed of quantitative entries taken at regular intervals over a period of time. Use a time series chart to display the data. Example (#32): Ground Beef prices: ‘94‘95‘96‘97‘98‘99‘00‘01‘02‘03‘04‘05 1.381.401.421.39 1.531.631.711.692.232.142.30

13. Grinnell College Main Issues Discussed: (1) Population: are we interested in all chocolate chip cookies on the market including the cookie dough you bake yourself, soft and hard cookies? (2) Sample and sample size: How many varieties and which ones do we choose? (3) Details: How blind do we need to make the test. Do the subjects need to be literally blind-folded or can the appearance of the cookie be part of what they are reacting to? Does the researcher need to be blind to which cookies are which? (4) Measurement: Do we make subjects rank cookies or rate them on a 5 or 7 point scale? What is/are the independent variable(s)? Taste, texture, appearance, overall rating? What is the independent variable? Price per ounce or per cookie?

14. Last Time: Let's devise an experiment to see if for commercially available chocolate chip cookies price translates into quality. Devise an experiment to answer this question. Work in small groups to come up with a plan for the experiment. Generate your ideas for a good experiment with as much detail as possible.

15. Sample Rating Sheet from Grinnell College COOKIE DATA SHEET -- Your filling out of this form indicates consent to participate in the experiment. NAME: ______________________________________________ __ 1. I buy a package of commercial chocolate chip cookies on the average about: (a) once per week, (b) less than once a week but at least once per month (c) less than once per month CIRCLE ONE 2. My preferred brand of chocolate chip cookies is: (Put "no preference" in appropriate). 3. I am MALE FEMALE (cirle one) RATINGS (circle) according to: P = poor F = fair G = good VG = Very good E = excellent TASTE TEXTURE APPEARANCE OVERALL