Analyzing Categorical Data & Displaying Quantitative Data Section 1.1 & 1.2 Reference Text: The Practice of Statistics, Fourth Edition. Starnes, Yates, Moore
Starter Problem Antoinette plays a lot of golf. This summer she got a new driver and kept track of how far she hit her tee shots in several rounds. Look at these data (drive lengths in yards) and then write a few sentences that describe the lengths of her drives: 246 260 230 233 254 203 223 193 238 220 210 237 270 240 192 204 250 274 220 240 235 250 222 230 225 241 225 230 250 200 250 226 240
Today s Objectives Analyze pie charts and bar graphs Two way tables: Marginal Distribution Conditional Distribution A Titanic Disaster Analyze Dot Plots Describe CUSS your new best friend Stem and Leaf Plots: single, and back to back Histograms California Standard 14.0 Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line graphs and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots.
Types of Variables Categorical variables record which group or category an individual belongs to. What color is your hair? What year are you in school? What city do you live in? Did the tee shot land in the fairway? It does NOT make sense to average the results. Quantitative variables take on numeric values. How tall is a person? What score did a person get on the SAT? How many desks are in a room? How long was the tee shot? It DOES make sense to average the results.
Visual Representation of Categorical Variables Categorical variables are typically represented by pie charts (for percents) or bar charts (percents or counts). Married? Count (M) Percent Single 41.8 22.6 Married 113.3 61.1 Widowed 13.9 7.5 Divorced 16.3 8.8 150 100 50 0 S M W D Millions Single Married Widowed Divorced
Dilbert comics Use a pie chart only when you want to emphasize each category s relation to the whole. Pie charts are awkward to make by hand, but technology will do the job for you.
What Makes a Good Bar Graph? Good All bars have the same width X & Y axis labeled Units Title of Graph Bad Bars have different widths Pictures replacing the bars No labels Turn to Pg 11 in Text
Two Way Tables Marginal Distribution The marginal distribution of one of the categorical variables in a two way table of counts is the distribution of values of that variable among all individuals described by the table For example: data that has both Male and Female data, marginal dist. would be just looking at males compared to EVERYONE Example: Pg 12
Two Way Tables Conditional Distribution A conditional distribution of a variable describes the values of that variable among individuals who have specific value of another variable. There is a separate conditional dist. For each value of the other variable. For Example: Male & Females, just looking at the females and comparing the females amongst the different categories. Example pg 14
A Titanic Disaster: Activity Please turn to page 19 in your text book What to do: 1) What is the percent of people who survived? Is this a marginal or conditional, write a complete sentence! 2) Given the passenger survived, what are the percentages for each class? Is this a marginal or conditional, write a complete sentence! 3) Of those who died in first class, what percent of them were males? Females?
Break! -5 Minutes
Section 1.2: Quantitative Data w/ Graphs Dotplots CUSS Histograms Stemplots
Types of Variables Categorical variables record which group or category an individual belongs to. What color is your hair? What year are you in school? What city do you live in? Did the tee shot land in the fairway? It does NOT make sense to average the results. Quantitative variables take on numeric values. How tall is a person? What score did a person get on the SAT? How many desks are in a room? How long was the tee shot? It DOES make sense to average the results.
Visual representation of Quantitative Variables: Dotplots The most basic method is a dotplot. Every data point can be seen on the plot. Construction method: Draw a horizontal axis with a scale that covers the full range of values for the variable. Put a dot on (or above) the axis for each data point. If data duplicate, stack them vertically. Construct a dotplot now of Antoinette s drives: 246 260 230 233 254 203 223 193 238 220 210 237 270 240 192 204 250 274 220 240 235 250 222 230 225 241 225 230 250 200 250 226 240
Dotplot of Drive Data Collection 1 Dot Plot Based on the dotplot, estimate the center. We see it around 230 or 240 yards. Estimate the spread. Roughly from 190 to almost 280, so spread is about 90 yards. Describe the shape. 200 220 240 260 280 CalDrives It appears mound-shaped with most of the data clustered at the center and with tails at each end.
C: Center Median, where is it? C.U.S.S Mean can also describe the center, but is not resistant U: Unusual data points S: Spread S: Shape Outliers! Are there any? We can calculate them later in 1.3 Describe the variability of the graph (largest value smallest value) How many peaks? Is the data clumped in a general location? Is data stretching to the right (skewed right). Is the data stretching to the left (skewed left). LASTLY Always, ALWAYS C.U.S.S it out when describing graphs of data
Histograms Another important method is a histogram. Individual data points cannot be seen on the plot. Many data points are grouped together in vertical bars. Construction method: Draw a horizontal axis with a scale that covers the full range of values for the variable. Decide bar width (also called class width) so that 5 to 10 bars will cover the full range of data. Set borders for bars, count frequencies, draw bars. Use a vertical axis to show the bar height.
Histogram of Drive Data Collection 1 8 Histogram 7 6 5 Count 4 3 2 1 180 200 220 240 260 280 300 CalDrives From a visual examination, estimate the center, unusual points, spread and the shape. (CUSS) As before, you should see the center around 230 to 240, no unusual points, the spread looks like 90, and the shape still looks like a mound.
Stemplots AKA: Stem & Leaf Plots One way to organize numerical data is to make a stemplot. Lets turn to the board and walk through how to make a stemplotof the following data, found on pg33 50 26 26 31 57 19 24 22 23 38 13 50 13 34 23 30 49 13 15 51
Stemplots check list Did we make a stemplot? Did we talk about splitting stems 1122334455 upper and lower bounds Did we talk about back to back stemplots? Good now we can move on
Percent of Population Over 65 by State 4 9 5 Note: 4 9 = 4.9% 6 7 8 8 9 10 0 0 2 9 11 0 1 1 3 4 4 4 6 9 12 0 0 3 4 4 5 5 5 6 6 6 6 13 0 1 3 3 4 4 5 6 7 7 9 9 9 14 2 3 4 5 5 15 2 3 7 9 16 17 18 6
Today s Objectives Analyze pie charts and bar graphs Two way tables: Marginal Distribution Conditional Distribution A Titanic Disaster Analyze Dot Plots Describe CUSS your new best friend Stem and Leaf Plots: single, and back to back Histograms California Standard 14.0 Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line graphs and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots.
Homework Review pages 8-42 in the text. The Practice of Statistics, Fourth Edition. Starnes, Yates, Moore TB PG 22: 9, 11, 14,15,18,20 TB PG 42: 37,45,49,59,62,69,70,72-74 Herring s Workbook PG 4&5 Use 8.5x11 binder paper Follow homework guidelines