Role of Statistics & Graphical Methods for Describing Data

1. Chapter 1 & 3The Role of Statistics&Graphical Methods for Describing Data

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

3. Suppose we wanted to know the average GPA of high school graduates in the nation this year. We could collect data from all high schools in the nation. What term would be used to describe “all high school graduates”?

4. Population The entire collection of individuals or objects about which information is desired A census is performed to gather about the entire population What do you call it when you collect data about the entire population?

5. Suppose we wanted to know the average GPA of high school graduates in the nation this year. We could collect data from all high schools in the nation. Why might we not want to use a census here? If we didn’t perform a census, what would we do?

6. Sample A subset of the population, selected for study in some prescribed manner What would a sample of all high school graduates across the nation look like? A list created by randomly selecting the GPAs of all high school graduates from each state.

7. Once we have collected the data, what would we do with it? Suppose we wanted to know the average GPA of high school graduates in the nation this year. We could collect data from a sample of high schools in the nation.

8. Descriptive statistics the methods of organizing & summarizing data If the sample of high school GPAs contained 10,000 numbers, how could the data be described or summarized? • Create a graph • State the range of GPAs • Calculate the average GPA

9. Suppose we wanted to know the average GPA of high school graduates in the nation this year. We could collect data from a sample of high schools in the nation. Could we use the data from this sample to answer our question?

10. Inferential statistics involves making generalizations from a sample to a population Based on the sample, if the average GPA for high school graduates was 3.0, what generalization could be made? The average national GPA for this year’s high school graduate is approximately 3.0. Could someone claim that the average GPA for PISD graduates is 3.0? Be sure to sample from the population of interest!! No. Generalizations based on the results of a sample can only be made back to the population from which the sample came from.

11. Variable any characteristic whose value may change from one individual to another Is this a variable . . . The number of wrecks per week at the intersection outside?

12. Data observations on single variable or simultaneously on two or more variables For this variable . . . The number of wrecks per week at the intersection outside . . . What could observations be?

13. Types of variables

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

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

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

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

18. Classifying variables by the number of variables in a data set Suppose that the PE coach records the heightof each student in his class. Univariate - data that describes a single characteristic of the population This is an example of a univariate data

19. Classifying variables by the number of variables in a data set Suppose that the PE coach records the height and weightof each student in his class. Bivariate - data that describes two characteristics of the population This is an example of a bivariate data

20. Classifying variables by the number of variables in a data set Suppose that the PE coach recordsthe height, weight, number of sit-ups, and number of push-upsfor each student in his class. Multivariate - data that describes more than two characteristics (beyond the scope of this course) This is an example of a multivariate data

21. the appraised value of homes in Niceville the color of cars in the teacher’s lot the number of calculators owned by students at your school the zip code of an individual the amount of time it takes students to drive to school Identify the following variables: Discrete numerical Is money a measurement or a count? Categorical Discrete numerical Categorical Continuous numerical

22. Graphs for categorical data

23. Bar Graph • Used for categorical data • Bars do not touch • Categorical variable is typically on the horizontal axis • Frequency or relative frequency is on the vertical 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 Relative frequency = frequency / total

24. 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

25. Using class survey data: graph favorite ice cream graph birth month

26. Graphs for numerical data

27. 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

28. Distribution Activity . . .

29. Types (shapes)of Distributions

30. 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

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

32. 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

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

34. How to describe a numerical, univariate graph

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

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

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

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

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

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

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

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

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

44. More graphs for numerical data

45. 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?

46. 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?

47. 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.

48. 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 gum chewed per day by AP Stat students? Why or why not?

49. The two histograms below display the distribution of heights of gymnasts and the distribution of heights of female basketball players. Which is which? Why? Heights – Figure A Heights – Figure B

50. Suppose you found a pair of size 6 shoes left outside the locker room. Which team would you go to first to find the owner of the shoes? Why? Suppose a tall woman (5 ft 11 in) tells you she is looking for her sister who is practicing in the gym. To which team would you send her? Why?