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Data Analysis in Statistics: Graphs, Distributions, and Normal Models

Learn how to analyze data using graphs, distributions, and normal models. Understand variables, categorical vs. quantitative data, and measures of center and spread. Discover how to identify outliers and use the normal model for statistical analysis.

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Data Analysis in Statistics: Graphs, Distributions, and Normal Models

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  1. Jeopardy Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 $100 $100 $100 $100 $100 $200 $200 $200 $200 $200 $300 $300 $300 $300 $300 $400 $400 $400 $400 $400 $500 $500 $500 $500 $500 Final Jeopardy

  2. 1 - $100 • Name the W’s • Who, What, When, Where, Why, How

  3. 1 - $200 • What are the 2 types of variables discussed in chapter 1? • Categorical and quantitative

  4. 1 - $300 • What is the difference between categorical and quantitative data? • Categorical – categories.. Quantitative – can be measured in units

  5. 1 - $400 • The class is given a survey asking for: gender, number of siblings, and number of states visited. What are the variables and what type of variable are they? • Gender – Categorical….. Siblings – Quantitative …. States - Quantitative

  6. 1 - $500 • Dr. Engle distributed a survey (on paper) to all advisory classes (grades 9-12) at Clear Lake High School to find out how students got to & from school (car, walk, bike, bus). What ‘w’ is missing? • When

  7. 2 - $100 • What graphs best display categorical data? • Pie graph, bar graph, segmented bar graph

  8. 2 - $200 • What is the difference between a frequency table and a relative frequency table? • Relative frequency shows percent compared to the group, frequency shows count number

  9. 2 - $300 • Find the marginal distribution of survival rate • Alive – 711/2201 = 32.2% • Dead – 1490/2201 = 67.7%

  10. 2 - $400 • Find the conditional distribution of classes that survived. • 1st – 203/711 = 28.55% 2nd – 118/711 = 16.6% • 3rd – 178/711 = 25.03% • Crew– 212/711 = 29.82%

  11. 2 - $500 • What percent of the crew were survivors? • 212/885 = 23.95%

  12. 3 - $100 • What graphs best display quantitative data? • Histogram, stem and leaf, dot plot, box and whisker

  13. 3 - $200 • What 5 numbers are used in the box plot? • 5 number summary – Min, Q1, Median, Q3, Max

  14. 3 - $300 • What is the benefit of using stem and leaf over a histogram? • Stem and leaf preserve the individual data values, histograms show ranges

  15. 3 - $400 • What 4 things do we discuss when describing a distribution? • Shape, unusual (outliers), center, spread

  16. 3 - $500 • What would be the appropriate measure of center and spread for the following graph? Why? • Median and IQR ; outliers present

  17. 4 - $100 • What measure of center and spread will be effected by outliers? • Mean and Standard deviation

  18. 4 - $200 • Which boxplot has the higher median? What is it? • Set A, 11

  19. 4 - $300 • Which boxplot has a larger IQR? What is it? • Set B, 6

  20. 4 - $400 • How can we use calculations to see if there are any outliers? • Q1 – 1.5(IQR) = Lower fence • Q3 + 1.5(IQR) = Upper fence • Anything outside of these fences = outlier

  21. 4 - $500 • Does this set of data have any outliers? • Min: 0 Q1: 9 Med: 13 Q3: 17 Max:28 • No, all values fall between the fences

  22. 5 - $100 • What two things do we look for when deciding if we can use a normal model? • Symmetric, unimodal, outliers

  23. 5 - $200 • What % make up the rule for the normal model, and how many standard deviations away from the mean do you need to go for each? • 68% – 1 stdev both directions • 95% - 2 stdev away both directions • 99.7% - 3 stdev away both directions

  24. 5 - $300 • When given a normal model, find P ( z < 0.8 ) • 0.788 or 78.8%

  25. 5 - $400 • What is the z score of the 43rd percentile under the normal curve? • Z = -.176

  26. 5 - $500 • Test 1: mean = 87.5 s = 3 • Test 2: mean = 91.0 s = 2.5 • Joe made a 90 on test 1 and a 92 on test 2. Which test did he do “better” on? Give both z scores for proof. • Test 1: z = .8 Test 2: z = .4 • Joe was more successful than the class average by .8 standard deviations on test 1, so he did “better” on test 1.

  27. Final Jeopardy • Given the normal model below, what z scores hold the middle 50% of the data? Hint: think IQR • -0.67 < z < 0.67

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