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

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

  17. Methods of Travel BAR GRAPH EXAMPLE

  18. 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 Stacked Bar Graph

  19. Number of Toys Purchased

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

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

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

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

  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 • Details Later

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

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

  30. 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 Stem and Leaf Plot

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

  33. HISTOGRAM EXAMPLE

  34. 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 Box and Whisker Plots

  35. Weights of children to age 10

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

  37. Number of blankets sold each year

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

  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 Rabbits born in a month 1 2 3 4 5Week

  41. Normal Distribution

  42. Normality Plot

  43. Questions???? • The end!!!

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