Understanding Statistics: Describing Data Graphically

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 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. 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. 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 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. 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 SHS 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. 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

19. the appraised value of homes in Fort Smith 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

20. Graphs for categorical data

21. 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

22. Segmented Bar Charts • Instead of a circle, uses a rectangular bar to represent entire data set • Divided into segments representing different categories • Each segment is proportional to relative frequency for that category

23. Using class survey data:graph favorite subject graph gender & favorite subject

24. A frequency distribution for categorical data is a table that displays the possible categories along with the associated frequencies and/or relative frequencies. The frequency for a particular category is the number of times the category appears in the data set. The relative frequency for a particular category is the fraction or proportion of the observations resulting in the category.

28. 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

30. Graphs for numerical data

31. 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

32. Distribution Activity . . .

33. Types (shapes)of Distributions

34. 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

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

36. 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

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

38. How to describe a numerical, univariate graph

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

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

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

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

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

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

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

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

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

48. Describing Quantitative Data Histograms Boxplots Dotplots Stem and Leaf Plots

49. Just CUSS and BS!

50. Center “the typical value” Mean Median Unusual Features Gaps Outliers