Chapter 1 Exploring Data

1. Chapter 1 Exploring Data

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

3. Descriptive statistics *the methods of organizing & summarizing data

4. Inferential statistics *involves making generalizations from a sample to a population

5. Individuals *The objects described by a set of data.

6. Variable *Any characteristic of an individual that may change from one individual to another.

7. Data *observations on single variable or simultaneously on two or more variables

8. Types of variables

9. Categorical variables *or qualitative *identifies basic differentiating characteristics of the population Places individuals in categories.

10. Quantitative variables *or numerical *observations or measurements take on numerical values *would make sense to find an average *two types - discrete & continuous

11. Discrete (quantitative) *listable set of values *usually counts of items

12. Continuous (quantitative) *data can take on any values in the domain of the variable *usually measurements of something

13. 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

14. Identify the following variables: • the income of adults in your city • the color of M&M candies selected at random from a bag • the number of speeding tickets each student in AP Statistics has received • the area code of an individual • the birth weights of female babies born at a large hospital over the course of a year Quantitative Categorical Quantitative Categorical Quantitative

16. Distribution *tells us what values the variable takes and how often it takes these values.

17. Data Analysis From Data Analysis to Inference Population Sample Collect data from a representative Sample... Make an Inference about the Population. Perform Data Analysis, keeping probability in mind…

18. Activity: Hiring Discrimination Follow the directions on Page 5 Perform 5 repetitions of your simulation. Turn in your results to your teacher. Data Analysis

19. Graphs for categorical data

20. Analyzing Categorical Data Displaying categorical data Frequency tables can be difficult to read. Sometimes is is easier to analyze a distribution by displaying it with a bar graph or pie chart.

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

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24. Pie (Circle) Chart *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

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26. Two-Way Tables *Describes two categorical variables.

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28. Analyzing Categorical Data Marginal Distributions The distribution of values described by the table. • Note: Percents are often more informative than counts, especially when comparing groups of different sizes. • To examine a marginal distribution, • Use the data in the table to calculate the marginal distribution (in percents) of the row or column totals. • Make a graph to display the marginal distribution.

29. Marginal Distributions

30. Relationships Between Categorical Variables Definition: A Conditional Distribution of a variable describes the values of that variable among individuals who have a specific value of another variable. • To examine or compare conditional distributions, • Select the row(s) or column(s) of interest. • Use the data in the table to calculate the conditional distribution (in percents) of the row(s) or column(s). • Make a graph to display the conditional distribution. • Use a side-by-side bar graph or segmented bar graph to compare distributions.

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37. Organizing a Statistical Problem As you learn more about statistics, you will be asked to solve more complex problems. How to Organize a Statistical Problem: A Four-Step Process State: What’s the question that you’re trying to answer? Plan: How will you go about answering the question? What statistical techniques does this problem call for? Do: Make graphs and carry out needed calculations. Conclude: Give your practical conclusion in the setting of the real-world problem.

38. Graphs for quantitative data

39. 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

41. Examining the Distribution of a Quantitative Variable • In any graph, look for the overall pattern and for striking departures from that pattern. • Describe the overall pattern of a distribution by its: • Center • Unusual Occurrences (Typically outliers) • Shape • Spread Don’t forget to CUSS in context!!

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

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

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

45. 2. Unusual occurrences *outliers - value that lies away from the rest of the data *gaps *clusters *anything else unusual

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

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

48. 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

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50. Uniform *refers to data in which every class has equal or approximately equal frequency