The Role of Statistics & Graphical Methods for Describing Data

1. The 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 something about the GPAs 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. Why might we not want to use a census here? Suppose we wanted to know something about the GPAs of high school graduates in the nation this year. We could collect data from all high schools in the nation. 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 something about the GPAs 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 something about the GPAs 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. involves making generalizations from a sample to a population Inferential statistics 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 DISD 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. any characteristic whose value may change from one individual to another Variable Is this a variable . . . The number of wrecks per week at the intersection outside?

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

13. 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

14. 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 see is looking for her sister who is practicing with a gym. To which team would you send her? Why? What aspects of the graphs helped you answer these questions?

15. Types of variables

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

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

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

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

20. 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

21. the appraised value of homes in DeSoto 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 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 • 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

24. Using class survey data:graph popular TV shows graph gender & drug use

25. 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

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

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

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

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

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

40. More graphs for numerical data

41. 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?

42. 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?

43. 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.

44. 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?

45. 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