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Chapter 1 & 3

Chapter 1 & 3. Statistics. the science of collecting, analyzing, and drawing conclusions from data. Descriptive statistics. the methods of organizing & summarizing data. Inferential statistics. involves making generalizations from a sample to a population. Population.

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Chapter 1 & 3

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  1. Chapter 1 & 3

  2. Statistics the science of collecting, analyzing, and drawing conclusions from data

  3. Descriptive statistics the methods of organizing & summarizing data

  4. Inferential statistics involves making generalizations from a sample to a population

  5. Population The entire collection of individuals or objects about which information is desired

  6. Sample A subset of the population, selected for study in some prescribed manner

  7. Variable any characteristic whose value may change from one individual to another

  8. Data observations on single variable or simultaneously on two or more variables

  9. Types of variables

  10. Categorical variables • or qualitative • identifies basic differentiating characteristics of the population

  11. Numerical variables • or quantitative • observations or measurements take on numerical values • makes sense to average these values • two types - discrete & continuous

  12. Discrete (numerical) • listable set of values • usually counts of items

  13. Continuous (numerical) • data can take on any values in the domain of the variable • usually measurements of something

  14. Classification by the number of variables • Univariate - data that describes a single characteristic of the population • Bivariate - data that describes two characteristics of the population • Multivariate - data that describes more than two characteristics (beyond the scope of this course

  15. the income of adults in your city the color of M&M candies selected at random from a bag the number of speeding tickets each student in AP Statistics has received the area code of an individual the birth weights of female babies born at a large hospital over the course of a year Identify the following variables: Numerical Categorical Numerical Categorical Numerical

  16. Graphs for categorical data

  17. Bar Graph • Used for categorical data • Bars do not touch • Categorical variable is typically on the horizontal axis • To describe – comment on which occurred the most often or least often • May make a double bar graph or segmented bar graph for bivariate categorical data sets

  18. Using class survey data:graph birth month graph gender & handedness

  19. Pie (Circle) graph • Used for categorical data • To make: • Proportion 360° • Using a protractor, mark off each part • To describe – comment on which occurred the most often or least often

  20. Graphs for numerical data

  21. Dotplot • Used with numerical data (either discrete or continuous) • Made by putting dots (or X’s) on a number line • Can make comparative dotplots by using the same axis for multiple groups

  22. Distribution Activity . . .

  23. Types (shapes)of Distributions

  24. Symmetrical • refers to data in which both sides are (more or less) the same when the graph is folded vertically down the middle • bell-shaped is a special type • has a center mound with two sloping tails

  25. Uniform • refers to data in which every class has equal or approximately equal frequency

  26. Skewed (left or right) • refers to data in which one side (tail) is longer than the other side • the direction of skewness is on the side of the longer tail

  27. Bimodal (multi-modal) • refers to data in which two (or more) classes have the largest frequency & are separated by at least one other class

  28. How to describe a numerical, univariate graph

  29. What strikes you as the most distinctive difference among the distributions of exam scores in classes A, B, & C ?

  30. 1. Center • discuss where the middle of the data falls • three types of central tendency • mean, median, & mode

  31. Class What strikes you as the most distinctive difference among the distributions of scores in classes D, E, & F?

  32. 2. Spread • discuss how spread out the data is • refers to the variability of the data • Range, standard deviation, IQR

  33. What strikes you as the most distinctive difference among the distributions of exam scores in classes G, H, & I ?

  34. 3. Shape • refers to the overall shape of the distribution • symmetrical, uniform, skewed, or bimodal

  35. K What strikes you as the most distinctive difference among the distributions of exam scores in class K ?

  36. 4. Unusual occurrences • outliers - value that lies away from the rest of the data • gaps • clusters • anything else unusual

  37. 5. In context • You must write your answer in reference to the specifics in the problem, using correct statistical vocabulary and using complete sentences!

  38. More graphs for numerical data

  39. Stemplots (stem & leaf plots) • Used with univariate, numerical data • Must have key so that we know how to read numbers • Can split stems when you have long list of leaves • Can have a comparative stemplot with two groups Would a stemplot be a good graph for the number of pieces of gun chewed per day by AP Stat students? Why or why not? Would a stemplot be a good graph for the number of pairs of shoes owned by AP Stat students? Why or why not?

  40. Example: The following data are price per ounce for various brands of dandruff shampoo at a local grocery store. 0.32 0.21 0.29 0.54 0.17 0.28 0.36 0.23 Can you make a stemplot with this data?

  41. Example: Tobacco use in G-rated Movies Total tobacco exposure time (in seconds) for Disney movies: 223 176 548 37 158 51 299 37 11 165 74 9 2 6 23 206 9 Total tobacco exposure time (in seconds) for other studios’ movies: 205 162 6 1 117 5 91 155 24 55 17 Make a comparative stemplot.

  42. Histograms • Used with numerical data • Bars touch on histograms • Two types • Discrete • Bars are centered over discrete values • Continuous • Bars cover a class (interval) of values • For comparative histograms – use two separate graphs with the same scale on the horizontal axis Would a histogram be a good graph for the fastest speed driven by AP Stat students? Why or why not? Would a histogram be a good graph for the number of pieces of gun chewed per day by AP Stat students? Why or why not?

  43. Cumulative Relative Frequency Plot(Ogive) • . . . is used to answer questions about percentiles. • Percentiles are the percent of individuals that are at or below a certain value. • Quartiles are located every 25% of the data. The first quartile (Q1) is the 25th percentile, while the third quartile (Q3) is the 75th percentile. What is the special name for Q2? • Interquartile Range (IQR) is the range of the middle half (50%) of the data. IQR = Q3 – Q1

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