Warm Up: What is Statistics?

Intro: What is Stats? Statistics: Data: The science (and art) of learning from data. Data: Numbers with a contextual meaning. We use data and Statistics to draw conclusions about a population based on sample information. Data/Statistics Population Inference/Conclusions Sample

Important Terms Population – the group we wish to study Sample – a portion or small group from the population Census – data on everyone in a population Anecdote – limited information about a population, often misleading

4 Themes of Stats Part I: Exploratory Data Analysis The tools and strategies for organizing, displaying, describing, and analyzing data. Part II: Producing Data Designing surveys, experiments, and observational studies that will yield the data necessary to answer a question of interest. Part III: Probability The study of chance behavior. How likely are certain outcomes? Part IV: Inference Draw conclusions about the population based on samples. Test claims and compute estimates.

Traditional Math vs. Stats Focused on calculation/process Usually one correct answer Statistics: Focused on understanding what the answer means A lot of reading and writing

Chapter 1 - Important Terms Individuals – Objects described by a set of data. Could be people, animals, computer chips, etc. Variable – Characteristics of an individual Categorical variable – places individual into one of several groups Quantitative variable – numerical value describing an individual

Example A sample of cars was taken from those parked in the student parking lot. The following characteristics were recorded for each car: Model, mileage on odometer, color, length of wheelbase, age, and gender of the owner What are the individuals in this data set? b) Which variables are categorical and which are quantitative?

Displays of Categorical Data – Bar Graph A Zagat survey from 2014 asked Americans their favorite type of pizza. NY Thin Crust 39% Neapolitan 17% Chicago Deep Dish 9% Chicago Thin Crust 7% California 5% Other 23% 1) Plot counts or percentages. 2) Always label axes and show scales. 3) Leave a gap between the bars.

Displays of Categorical Data – Pie Chart A Zagat survey from 2014 asked Americans their favorite type of pizza. NY Thin Crust 39% Neapolitan 17% Chicago Deep Dish 9% Chicago Thin Crust 7% California 5% Other 23% 1) Only plot percentages on a pie chart. 2) You need 100% of the data to make a pie chart. 3) We won’t make pie charts by hand.

Example A Gallup Poll in 2016 asked 1015 adults the following question: “What do you think is the best long-term investment?” The table below lists the proportion of adults that chose each category. Bonds 0.07 Real Estate 0.35 Gold 0.17 Savings 0.15 Other 0.04 Stocks & Mutual Funds 0.22 1) Use the data to make a bar graph, arranged from largest to smallest percentage. 2) Could you make a pie chart with this data? Why or why not?

Other Displays of Categorical Data If we measure 2 variables for each individual in our data set, we may create some additional displays: 1) Side-by-side Bar Graph 2) Segmented Bar Graph 3) Mosaic Plot An on-line survey from 2017 asked 700 women and 300 men their favorite color: Women Men Blue 0.26 0.29 Green 0.17 0.20 Purple 0.17 0.09 Red 0.12 0.14 Orange 0.07 0.08 Yellow 0.06 0.04 Other 0.15 0.16

Categorical Data from this Class On the board place a tally mark under the correct category to answer the following question: Where did you travel to this summer? a) I stayed in California. b) I traveled to other states but remained in the U.S. c) I traveled to another country.

Categorical Data from this Class Using the data from the class make one of the following plots: 1) Side by side Bar Graph 2) Stacked Bar Graph 3) Mosaic Plot You may make any type of plot that you wish, however at least one person from each table has to make each type of plot. (Remember to graph proportions, not raw counts.)