Analyze the following graph!

1. Analyze the following graph!

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

3. 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

4. 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.

5. Types of variables

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

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

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

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

10. 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

11. 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

12. 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

13. the appraised value of homes in Plano 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

14. Types (shapes)of Distributions

15. 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

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

17. 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

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

19. How to describe a numerical, univariate graph

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

21. Scatter Plots Time Plots Scatter Plots – Start by placing the explanatory variable on the x-axis, and the response variable on the y-axis. Then plot each point, and look for tendencies. Positive linear correlation, Negative quadratic correlation, ect. Time Plots – Place the time on the x-axis, and the amount of the y-axis. Plot each point and then connect them. We utilize these to analyze trends as well.