What is Statistics?Statistics is the science of: Collecting data Analyzing data Drawing conclusions from data
Statistics include numerical facts andfigures such as: The largest earthquake measured 9.2 on the Richterscale. Men are at least 10 times more likely than women tocommit murder. One in every 8 South Africans is HIV positive. By the year 2020, there will be 15 people aged 65and over for every new baby born.
Why should we study statistics? We want to make sense of the world. We don’t want to be lied to. We want to be able to spot trends that help us makegood decisions.
4 Main Themes:I. Exploring data (compare graphs and numbers)II. Sampling & Experimentation (collect data)III. Anticipating Patterns (Probability and Simulation)IV. Statistical Inference (Make conclusions)
Individuals are the objects described by a set of data. Variable is any characteristic of an individual.EXAMPLE: An AP Statistics class list contains informationabout the students enrolled. The students enrolled are theindividuals, and for each individual, there are variablessuch as student number, gender and home phone number.
Check For Understanding You want to compare the “size of several AP statisticstextbooks. Give at least three possible numerical variablesthat describe the “size” of a book. In what units would youmeasure each variable?
Possible Answers (units) Number of pages (pages) Number of words (words) Volume (cubic inches, cubic centimeters) Height and/or width (pounds, ounces) Number of chapters (chapters) Weight (pounds, ounces)
Types of variables: A categorical variable places an individual into one ofseveral groups or categories. Examples: gender, letter grade, zip code A quantitative variable takes numerical values for whicharithmetic operations such as adding and averaging makesense. Examples: scores on a test, age, GPA
Check for Understanding Data from a medical study contain values of many variablesfor each of the people who were the subjects of the study.Which of the following variables are categorical and which arequantitative?(a) gender (female or male)(b) Age (years)(c) Race (Asian, black, white,or other)(d) Smoker (yes or no)(e) Systolic blood pressure (millimeters of mercury)(f) Level of calcium in the blood (micrograms per milliliter)
The distribution of a variable is a list (chart, picture,etc.) that tells us what values the variable takes andhow often it takes these values.Most variables take on values that vary. Sometimesthose values are clustered close together, and othertimes they are spread far apart. When we look athow those values vary, we are looking at thedistribution of the variable.
Important features of a distribution:Shape Is the distribution symmetric or skewed?Outliers Are there individual observation that falls outside the overallpattern of the graph?Center Is there a typical or most common value of the variable? Isthere a mode? Bimodal?Spread What is the range of possible values? How wide is thedistribution?
Check For UnderstandingThe histogram below shows thedistribution of total returns for all1528 stocks listed on the NewYork State Exchange in one year.(a) Describe the overall shape of thedistribution of total returns.(b) What is the approximate centerof this distribution? (For now,take the center to be the valuewith roughly half the stockshaving lower returns and halfhaving higher returns.)(c) Approximately what were thesmallest and largest totalreturns? (This describes thespread of the distribution)
Answers(a) Roughly symmetric, though it might be viewed as SLIGHTLYskewed to the right.(b) About 15%. (39% of the stocks had a total return less than10%, while 60% had a return less than 20%. This places thecenter of the distribution somewhere between 10% and20%.)(c) The smallest return was between -70% and -60%, while thelargest was between 100% and 110%.
When analyzing data,ask the following: Who are the individuals being described? What are the variables? Why were the data gathered? When, where, how, and by whom were the dataproduced?
Check For UnderstandingIn October 2005 Discover published an article on the colonies of ants. Theyreported some basic information about many species of ants and the results ofsome discoveries found by myrmecologist Walter Tschinkel of the University ofFlorida. Information included the scientific name of the ant species, thegeographic location, the depth of the nest (in feet), the number of chambers inthe nest, and the number of ants in the colony. The article documented how newant colonies begin, the ant-nest design, and how nests differ in shape, number,size of chambers, and how they are connected, depending on the species. Itreported that nest designs include vertical, horizontal, or inclined tunnels formovement and transport of food and ants.Describe the Ws, if the information is given. If the information is not given, statethat it is not specified. Who: What: When: Where: How: Why:
Answers Who: Colonies of ants. "Many species of ants," but noindication of exactly how many. What: scientific name, geographic location, average nestdepth, average number of chambers, average colony size,how new ant colonies begin, the ant-nest design, and hownests differ in architecture. When: October 2005 Where: not specified How: The results of some discoveries found by myrmecologistWalter Tschinkel of the University of Florida Why: Information of interest to readers of the magazine