Chapter 1 Introduction Analyzing Categorical Data

1 Chapter 11 Chapter 1 Introduction & : Analyzing Categorical DataIntroductionData Analysis: Making Sense of DataAfter this section, you should be able DEFINE Individuals and Variables DISTINGUISH between Categorical and Quantitative variables DEFINE Distribution DESCRIBE the idea behind Inference What is the Study of Statistics?! Statistics is the science of data . In this course we study four different aspects of statistics: data Analysis (Chapters 1 to 3) The process of organizing, displaying, summarizing, and asking questions about data . data Collection ( Chapter 4) The process of conducting and interpreting surveys and experiments. Anticipating Patterns/Probability ( Chapter 5 to 7) The process of using probability and chance to explain natural phenomena.

2 Inference( Chapter 8 to 12) The process of making predications and evaluations about a population from a data from a representative data Analysis, keeping probability in an inferenceabout the any characteristic of an individual or objectCategorical Variable Usually an adjective Rarely a numberExamples: Gender Race Grade in School (Sophomore, Jr., Sr.) Zip CodeQuantitative Variable Always a number Must be able to find the mean of the numbersExamples: Weight Height GPA # of AP Classes taken Square footageDistribution Distribution: describes what values a variable takes and how often it takes those values Essentially distribution replaces the words data or graph . The median of the distribution is 28. The distribution is skewed left. Dotplot of MPG DistributionChapter 12 Organizing a Statistical ProblemState:What s the question that you re trying to answer?

3 Plan:How will you go about answering the question? What statistical techniques does this problem call for?Do: Make graphs and carry out needed :Give your practical conclusion in the setting of the real world problem.**Using this method is NOT required; however, all complete answers MUST include the Do and Conclude steps**The Four Step ProcessSection Categorical DataAfter this section, you should be able CONSTRUCT and INTERPRET bar graphs and pie charts RECOGNIZE good and bad graphs CONSTRUCT and INTERPRET two way tables DESCRIBE relationships between two Categorical variables ORGANIZE statistical problemsDistribution & Categorical VariablesThe distribution of a Categorical variable lists the count or percent of individuals who fall into each Course CountEnglish8 Foreign Language4 Histroy11 Math15 Science12 Favorite Course PercentageEnglish16%Foreign Language8%Histroy22%Math30%Science24%Dis playing Categorical DataFrequency tables can be difficult to read.

4 Sometimes it is easier to analyze a distribution by displaying it with a bar graph or pie AP Exam ScoresChapter 13 Bar graphs compare several quantities by comparing the heights of bars that represent those eyes react to the areaof the bars as well as height. Be sure to make your bars equally the temptation to replace the bars with pictures for greater can be misleading!Graphs: Good and BadThis ad for DIRECTV has multiple problems. How many can you point out?Two Way Tables Two Way Tables: describe two Categorical variables, organizing counts according to a row variable and a column a dataset involves two Categorical variables, we begin by examining the counts or percents in various categories for oneof the variables. Member of No ClubsMember of One ClubMember of 2 or More ClubsTotalRides the School Bus553320108 Does not Ride Bus164482142 Total7177102250 What proportion of students that ride the school bus are members of two or more clubs?

5 What proportion of students that are members of no clubs do not ride the school bus? What proportion of students that do not ride the school bus are members of at least one club?Member of No ClubsMember of One ClubMember of 2 or More ClubsTotalRides the School Bus553320108 Does not Ride Bus164482142 Total7177102250 What proportion of males have a good chance at being rich? What proportion of females have a 50 50 chance at being rich? What proportion of young adults that have an almost certain chance of being rich are male?Comparing Categorical DistributionsSophomoreJuniorSeniorTotalO ne0044 Two131216 Three47617 Four74819 Five2035 Total14143361 Comparing Categorical Distributions0%20%40%60%80%100%Sophomore JuniorSeniorOneTwoThreeFourFiveChapter 14 Comparing Categorical Distributions0%20% 40% 60% 80% 100%Rides the School BusDoes not Ride BusMember of NoClubsMember of OneClubMember of 2 orMore ClubsWriting to Compare Categorical Distributions Cite specific numerical values/proportions.

6 Use comparison words. Greater, smaller, less, while only, more, wider, narrower, etc. Use transition words However, whereas, similarly, additionally, etc. Discuss at least two points of Categorical Distributions0%20% 40% 60% 80% 100%Rides the School BusDoes not Ride BusMember of NoClubsMember of OneClubMember of 2 orMore ClubsIs there an association between after school club participation and whether or not the student rides the school bus? Support your answer with a discussion of the provided Categorical DistributionsSample Answer:Yes, there is a clear association between after school club participation and transportation. Only 11% of students who don t ride the bus do not participate in after school clubs, whereas 51% of students who do ride the bus do not participate.

7 Similarly, 58% of students who do not ride the bus are involved in 2 or more clubs, while only 19% of students riding the bus are involved in 2 or more clubs. However, the proportion of students who participate in one club is the same for students who ride and students who don t ride the bus. : Displaying Quantitative data with GraphsSection Quantitative data with GraphsAfter this section, you should be able CONSTRUCT and INTERPRET dotplots, stemplots, and histograms DESCRIBE the shape of a distribution COMPARE distributions USE histograms wiselyChapter 15 Dotplots Each data value is shown as a dot above its location on a number of Goals Scored Per Game by the 2004 US Women s Soccer Team30278243511453113332122243561551151. Draw a horizontal axis (a number line) and label it with the variable Scale the axis from the minimum to the maximum Mark a dot above the location on the horizontal axis corresponding to each data to Make a DotplotIn any graph, look for the overall pattern and for striking departuresfrom that the overall pattern of a distribution by its: Shape Outliers Center SpreadDon t forget your SOCS!

8 Don t forget your SOCS!How to Describe Quantitative DataDescribing ShapeWhen you describe a distribution s shape, concentrate on the main features. Look for rough symmetryor clear Definitions:Symmetric: if the right and left sides of the graph are approximately mirror images of each to the right(right skewed) if the right side of the graph is much longer than the left to the left(left skewed) if the left side of the graph is much longer than the right leftSkewed rightChapter 16 Other Ways to Describe Shape: Unimodal Bimodal MultimodalOutliersDefinition: Values that differ from the overall pattern are outliers. We will learn specific ways to find outliers in a later Chapter . For now, we can only identify potential outliers. CenterWe can describe the center by finding a value that divides the observations so that about half take larger values and about half take smaller values.

9 Ways to describe center: Calculate median (best when distribution is skewed) Calculate mean (best when distribution is symmetric)SpreadThe spread of a distribution tells us how much variabilitythere is in the data . Ways to describe spread: Calculate the range IQR (coming later) Standard Deviation (coming later)Describe the shape, center, and spread of the distribution. Are there any potential outliers? Remember to include CONTEXT!!! Chapter 17 Sample Answer: Shape: The shape of the distribution is roughly unimodal and skewed left. Center: The mean is mpg and the median is 28 mpg. (only need one measure) Spread: The range is 19 mpg. Outliers: There are two potential outliers/influential values: 14 mpg and 18 (Stem and Leaf Plots)Stemplots give us a quick picture of the distribution while including the actual numerical )Separate each observation into a stem(all but the final digit) and a leaf(the final digit).

10 2)Write all possible stems from the smallest to the largest in a vertical column and draw a vertical line to the right of the )Write each leaf in the row to the right of its )Arrange the leaves in increasing order out from the )Provide a keythat explains in context what the stems and leaves to Make a StemplotStemplots (Stem and Leaf Plots)These data represent the responses of 20 female AP Statistics students to the question, How many pairs of shoes do you have? 50 26 26 31 57 19 24 22 23 3813 50 13 34 23 30 49 13 15 51 Two Special Types of Stem Plots Spilt Stemplots: Best when data values are bunched up Spilt 0 4 and 5 9 Back to Back Stemplot: Compares two distributions of the same quantitative variable001122334455 Key: 4|9 represents a student who reported having 49 pairs of 40 5556777781 000012412 2233 584455 Females33395433266410891007 split stems Back to BackHistograms Quantitative variables often take many values.