Warm-Up: Believe It or Not?

1. Warm-Up: Believe It or Not? • A student claims that they have flipped a fair coin 200 times and only had 84 times the heads side of the coin showed up.Do you believe this student or not, discuss with your neighbor why or why not.

2. Chapters 2 - 4The Role of Statistics&Graphical Methods for Describing Data

3. In order to learn Statistics, we need to learn the language of statistics first. We’ll be learning a lot of new vocabulary today – through examples and activities

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

5. 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.

6. 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”?

7. Population The entire group of individuals or objects we want information about A censusattempts to contact every individual in the entire population What do you call it when you collect data about the entire population?

8. 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.

9. 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?

10. Sample A part of the population that we actually examine in order to gather information 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.

11. 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.

12. 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.

13. 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

14. 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?

15. Inferential statistics involves making generalizations from a sample to a population Be sure to sample from the population of interest!!

16. 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 FISD graduates is 3.0? No. Generalizations based on the results of a sample can only be made back to the population from which the sample came from.

17. Variable any characteristic whose value may change from one individual or object to another

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

19. Data observations on a single variable or simultaneously on two or more variables

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

21. Variability The range of possible data values The goal of statistics is to understand the nature of variability in a population

22. Variability The range of possible data values The goal of statistics is to understand the nature of variability in a population Populations with no variability are rare and boring (of little statistical interest). Can you think of a population that has no variability?

23. Variability 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

24. 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) you see is looking for her sister who is practicing in the gym. To which team would you send her? Why?

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

26. Types of variables

27. Categorical variables • (qualitative) • Variables where the possible values are set of categories

28. Numerical variables • or quantitative • Variables where the values are numbers (are numerical) • (makes sense to average these values) • two types - discrete & continuous

29. Numerical: Discrete • Values are isolated points on a number line • usually counts of items

30. Numerical: Continuous • Set of possible values form an entire interval on the number line • usually measurements of something

31. 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

32. 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

33. 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

34. the appraised value of homes in Faraway 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: Continuous numerical Categorical Discrete numerical Categorical Continuous numerical

35. Warm-Up: Classifying variables Write an example of a variable on the index card provided (try to come up with something we have not discussed in class already). Please include your name. When done, fold your index card in half and place in the bowl in the back of the room. We will classify these before completing notes on display types.

36. Graphs for categorical data

37. Bar Graph • Used for categorical data • Bars do not touch • Categorical variable is typically on the horizontal axis • Best used to describe or 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

38. Comparative Bar Charts • Use relative frequency • If observations are the same for all groups (50 boys and 50 girls), you could use the frequency • Vertical scale the same always label both axis compare!!

39. Pie Chart (circle graph) • Used for categorical data • To make: • Proportion X 360° • Using a protractor, mark off each part • Best used to describe or comment on which occurred the most often or least often

40. Using class survey data, make bar graphs for:birth month gender & handedness

41. Graphs for numerical data

42. 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

43. Dotplot • To compare the weights of the males and females we put the dotplots on top of each other, using the same scales.

44. Using class survey data make dot plots of:# AP classes# siblings

45. Types (shapes)of Distributions

46. 1) 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

47. 2) Uniform • refers to data in which every class has equal or approximately equal frequency

48. 3) 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

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

50. Warm-Up: Example 1 (From Your Notes) • Looking at Example 1 (about sports-related injuries), complete the columns titled “Tally” and “Frequency”.