1. StatisticsStatistics Graphic distributions

2. What is Statistics? Statistics is a collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data.

3. Uses of Statistics “Some students choose it because it is required, but increasing numbers do so voluntarily because they recognize its value and application to whatsoever field they plan to pursue. Because employers love to see a statistics course on the transcript of a job applicant, you will have an advantage….” Mario F. Triola

4. Abuses of Statistics Small samples Precise numbers Guesstimates Distorted percentages Partial pictures Deliberate distortion

5. More Abuses Loaded questions Pictographs Bad Samples Pollster Pressure Misleading graphs

6. Example 1 of Misleading Graphs

7. Example 2 of Misleading Graphs

8. Exploratory Data Analysis Just as an explorer crossing unknown lands tells what he sees, we will be describing the data that we find. –Examine each variable –Describe relationship –Begin with a graph

9. Nature of Data Quantitative Data – (QUANTITY) Numbers representing counts or measurements Qualitative or Categorical Data – (QUALITY) Separated into different categories that can be divided into non-numeric characteristics

10. M&M activity Method of collecting data Weigh candies using a digitized scale, check color, and record.

11. Weights in grams of a sample of M&M candies.887.923.906.923.848.911.931.783.978.942.875.930.908.942.868.922.882.949.785.898.920.923.921.959.882.942.912.975.920.791.902.892.922

12. Data Categorical Binary CategoricalQuantitative

14. Types of Graphic Representations Frequency distribution Bar Graph Stacked Bar Graph Pie Charts Dot Plots Histograms Stem and Leaf Plot …

15. Box and Whisker Time Plot Scatter Plot Cumulative Plots Normality Plot Normal Distribution

16. Frequency Distribution Pattern of variation The distribution tells what values a variable takes and how often Raw Data

17. Frequency Distribution List of categories along with counts Colors in a bag of skittles Red14 Yellow21 Blue15 Green21 Purple17 Orange15

18. Bar Graph Use of Categorical data Attractive Heights show counts More flexible than pie charts Vertical and Horizontal Can distort values

19. Methods of Travel BAR GRAPH EXAMPLE

20. Stacked Bar Graph Used to distinguish two or more categories of the same variable Great for comparing/ contrasting two variables Can be a little difficult to distinguish size

21. Number of Toys Purchased

22. Pie Charts Visual Attractive Uses categorical data Easy to interpret Difficult to make precise Must use percents Close values difficult to differentiate

23. Flavors of Ice Cream PIE CHART EXAMPLE Guess what percentages these slices represent…

24. Flavors of Ice Cream PIE CHART EXAMPLE Were you close?

25. Dot Plots Good Visual Quantitative data Check for overall pattern Difficult with large amounts of data

26. Theme Park Attendance Per Day 35 404550556065707580859095100105 East Coast Resorts per thousand West Coast Resorts per thousand DOT PLOT EXAMPLE

27. Tools for Interpretation Don’t Forget your socks –SOCS S – Shape O –Check for outliers C – Describe the center S – Describe the spread

28. S – Shape Symmetric skewed left skewed right bimodal

29. O –Check for outliers Stuff that is outside of the normal range Details Later

30. C – Describe the center Values of central tendency: –Mean –Median –Mode –(Range)

31. S – Describe the spread –Symmetrical –Skewed –Uniform

32. Stem and Leaf Plot Sometimes data is too spread out to make a reasonable dot plot Five stems is a good minimum More flexible by rounding Easy to construct Hard with large data sets

33. Home Run Hits comparison Barry Hank Bonds vs. Aaron 9 6 1 3 5 5 4 2 0 4 6 7 9 7 7 4 4 3 3 3 0 2 4 4 8 9 9 9 6 2 0 4 0 0 4 4 4 4 5 7 5 6 3 717 = 17 hits

34. Histogram Quantitative variables Divides data into classes equal in size Visual may distort understanding

35. HISTOGRAM EXAMPLE

36. Box and Whisker Plots Easy to compare quartiles Outliers seen on modified boxplot Side by side = best comparison Difficult to determine size of data Can be misleading Show less detail

37. Weights of children to age 10

38. Time Plot Variables observed over time Horizontal axis has the time scale Check for overall pattern

39. Number of blankets sold each year

40. Scatter Plot Shows relationship of two variables Can determine overall tendencies Can determine strength of relationship Not all relationships are linear

41. Wife’s Age VS Husband’s Age

42. Cumulative Plots Also known as an ogive (“oh-jive”) Adds onto each progressive column Rabbits born in a month 1 2 3 4 5 Week Commonly confused with bar graphs

43. Normal Distribution

44. Normality Plot

45. Questions???? The end!!!