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Statistics

Statistics. Graphic distributions. 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. Uses of Statistics.

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Statistics

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  1. Statistics 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 • EX: • Qualitative or Categorical Data – (QUALITY) Separated into different categories that can be divided into non-numeric characteristics • EX:

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

  11. What variables are recorded here? • What type of variables are they?

  12. Types of Graphic Representations • Frequency Distribution • Bar Graph • Stacked Bar Graph • Pie Charts • Dot Plots • Histograms • Stem and Leaf Plot • …

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

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

  15. Frequency DistributionList of categories along with counts

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

  17. Methods of Travel BAR GRAPH EXAMPLE

  18. 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

  19. Number of Toys Purchased

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

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

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

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

  24. DOT PLOT EXAMPLE Theme Park Attendance Per Day East Coast Resorts per thousand West Coast Resorts per thousand

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

  26. S – Shape • Symmetric? • Skewed to the left? • Skewed to the right ? • Bimodal?

  27. O –Check for outliers • Stuff that is outside of the normal range • Exact details Later

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

  29. S – Describe the spread • IQR • Range • Standard Deviation • Wide spread? • Narrow Spread? • Uniform?

  30. 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

  31. Home Run Hits comparison • Barry Hank • Bonds vs. Aaron • 9 613 • 5 5 42 0 4 6 7 9 • 7 7 4 4 3 330 2 4 4 8 9 9 • 9 6 2 040 0 4 4 4 4 5 7 • 5 • 6 • 37 17 = 17 hits

  32. Histogram • Quantitative variables • Divides data into classes of equal size • Visual may distort understanding

  33. HISTOGRAM EXAMPLE

  34. 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

  35. Weights of children to age 10

  36. Time Plot • Does not show what happens WITHIN that time period! • Variables observed over time • Horizontal axis has the time scale • Check for overall pattern

  37. Number of blankets sold each year

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

  39. Wife’s Age VS Husband’s Age

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

  41. Normal Distribution

  42. Normality Plot

  43. Questions????

  44. Graph Exploration • Find five or more different graphs and identify the type you think it is.

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