Chapter 1, Chapter 2 (Section 2.1) Quiz Review
Terms ➢ Individuals: objects described by a set of data. ➢ Variable: any characteristic of these individuals ● Categorical Variable: places data into one of several groups or categories . ● Quantitative variable: takes numerical values for which arithmetic operations such as adding and averaging makes sense.
Example Name Sex Homeroom Grade Calculator # Test 1 Danny M Ms. Blair Senior B319 81 Francine F Mr. Kingsley Senior B298 92 Ricardo M Mrs. Alfonso Junior B304 87 ➢ Is Calculator number categorical or quantitative variable? ➢ Is Test 1 categorical or quantitative?
Exercise 1 Player Team Votes Points Height Position per (inches) Game Kevin Garnett Boston Celtics 2,399,148 18.8 83 Forward LeBron James Cleveland Cavaliers 2,108,831 30.0 80 Forward Dwight Howard Orlando Magic 2,066,991 20.7 83 Center Kobe Bryant Los Angeles Lakers 2,004,940 28.3 78 Guard Carmelo Anthony Denver Nuggets 1,723,701 25.7 80 Forward In the NBA, the fans vote to decide which player get to play in the NBA All-Star Game. Kevin Garnett of the Boston Celtics led all players, with 2,399,148 votes for the 2008 All-Star Game. The table below provides data about the top five vote-getters that year. (a)What individuals are measured?
Exercise 1 Player Team Votes Points Height Position per (inches) Game Kevin Garnett Boston Celtics 2,399,148 18.8 83 Forward LeBron James Cleveland Cavaliers 2,108,831 30.0 80 Forward Dwight Howard Orlando Magic 2,066,991 20.7 83 Center Kobe Bryant Los Angeles Lakers 2,004,940 28.3 78 Guard Carmelo Anthony Denver Nuggets 1,723,701 25.7 80 Forward In the NBA, the fans vote to decide which player get to play in the NBA All-Star Game. Kevin Garnett of the Boston Celtics led all players, with 2,399,148 votes for the 2008 All-Star Game. The table below provides data about the top five vote-getters that year. (a)What individuals are measured? NBA basketball players
Exercise 1 Player Team Votes Points Height Position per (inches) Game Kevin Garnett Boston Celtics 2,399,148 18.8 83 Forward LeBron James Cleveland Cavaliers 2,108,831 30.0 80 Forward Dwight Howard Orlando Magic 2,066,991 20.7 83 Center Kobe Bryant Los Angeles Lakers 2,004,940 28.3 78 Guard Carmelo Anthony Denver Nuggets 1,723,701 25.7 80 Forward In the NBA, the fans vote to decide which player get to play in the NBA All-Star Game. Kevin Garnett of the Boston Celtics led all players, with 2,399,148 votes for the 2008 All-Star Game. The table below provides data about the top five vote-getters that year. (b) What variables are recorded?
Exercise 1 Player Team Votes Points Height Position per (inches) Game Kevin Garnett Boston Celtics 2,399,148 18.8 83 Forward LeBron James Cleveland Cavaliers 2,108,831 30.0 80 Forward Dwight Howard Orlando Magic 2,066,991 20.7 83 Center Kobe Bryant Los Angeles Lakers 2,004,940 28.3 78 Guard Carmelo Anthony Denver Nuggets 1,723,701 25.7 80 Forward In the NBA, the fans vote to decide which player get to play in the NBA All-Star Game. Kevin Garnett of the Boston Celtics led all players, with 2,399,148 votes for the 2008 All-Star Game. The table below provides data about the top five vote-getters that year. (b) Quantitative or Categorical? In what units is each quantitative variable recorded? Team Votes PPG Height Position
Exercise 1 Player Team Votes Points Height Position per (inches) Game Kevin Garnett Boston Celtics 2,399,148 18.8 83 Forward LeBron James Cleveland Cavaliers 2,108,831 30.0 80 Forward Dwight Howard Orlando Magic 2,066,991 20.7 83 Center Kobe Bryant Los Angeles Lakers 2,004,940 28.3 78 Guard Carmelo Anthony Denver Nuggets 1,723,701 25.7 80 Forward In the NBA, the fans vote to decide which player get to play in the NBA All-Star Game. Kevin Garnett of the Boston Celtics led all players, with 2,399,148 votes for the 2008 All-Star Game. The table below provides data about the top five vote-getters that year. (b) Quantitative or Categorical? In what units is each quantitative variable recorded? Team; categorical Votes; (quantitative; units: votes) PPG; (quantitative; units: aver points per game) Height; (quantitative; units: inches) Position; categorical
Exercise 1 Player Team Votes Points Height Position per (inches) Game Kevin Garnett Boston Celtics 2,399,148 18.8 83 Forward LeBron James Cleveland Cavaliers 2,108,831 30.0 80 Forward Dwight Howard Orlando Magic 2,066,991 20.7 83 Center Kobe Bryant Los Angeles Lakers 2,004,940 28.3 78 Guard Carmelo Anthony Denver Nuggets 1,723,701 25.7 80 Forward In the NBA, the fans vote to decide which player get to play in the NBA All-Star Game. Kevin Garnett of the Boston Celtics led all players, with 2,399,148 votes for the 2008 All-Star Game. The table below provides data about the top five vote-getters that year. (c) Which variable or variables do you think most influence the number of votes received by an individual player?
Terms ➢ Population: the entire group of individuals about which we want information ➢ Sample: a part of the population from which we actually collect information, which is then used to draw conclusions about the whole ➢ Sample surveys: measure characteristics of some group of individuals (the population) by studying only some of its members (the sample) ● Survey a portion of the group to make a conclusion about the entire population
Terms ➢ Observational studies vs. Experiments ● What is the difference between the two? ● Specific?
Terms ➢ Observational study: a study that observes individuals and measures variables of interest but does not attempt to influence the responses. ➢ Experiment: purposely imposes some treatment on individuals in order to observe their responses. The purpose of an experiment is to study whether the treatment causes a change in the response.
Exercise 2 In 2001, researchers announced that “children who spend most of their time in child care are three times as likely to exhibit behavioral problems in kindergarten as those who are cared for primarily by their mothers.” (a) Was this likely an observational study or an experiment? Why? (b) Can we conclude that child care causes behavior problems? Why or why not?
Exercise 2 (a) An observational study. No treatment was imposed - children from different types pre-school training were simply compared. (b) No. There are other possible explanations for the behavioral differences between the children; for example, there may be more children with single parents who are in child care and this could be the reason for the behavioral problems.
Statistical Problem-Solving Process I. Ask a question of interest: A statistics question involves some characteristics that vary from individual to individual. I. Produce data: The methods of choice are observational studies and experiments. Analyze data: Graphs and numerical summaries are the tools for I. describing patterns in the data, as well as any deviations from those patterns. Interpret results: The results of the data analysis should help answer the I. question of interest.
Types of Graphs ➢ Bar graph and Pie Chart: good for categorical variables ➢ Histograms, Dot Plots, Time Plots, and Stemplots: good for quantitative variables.
Examples of Graphs (cont.) ➢ Histograms ➢ Dot Plots
Examples of Graphs (cont.) ➢ Time Plots: plots each observation against the time at which it was measured. ➢ Ogives Stemplots
Interpretation of Graphs We interpret a graph by describing the: - SPREAD - CENTER - SHAPE - PEAKS - ANY UNUSUAL FEATURES Spread : _____________________________________________________ Center : _____________________________________________________ Also known as the ____________
Interpretation of Graphs We interpret a graph by describing the: - SPREAD - CENTER - SHAPE - PEAKS - ANY UNUSUAL FEATURES Spread : the range, lowest and highest values Center : point where half the observations are above and half are below (median)
Interpretation of Graphs Cont’d Shape: symmetric : __________________________________________ skewed right : _____ side extends farther than ___ side most observations are on the ____ (toward ______ values) skewed left : ____ side extends farther than ____ side most observations are on the _____ (toward ______ values) NOTE: some distributions have shapes that are neither symmetric or skewed Peaks: which values are ____ common distributions can have few or many peaks
Interpretation of Graphs Cont’d Shape: symmetric : right and left side are approximate mirror images of each other skewed right : right side extends farther than left side most observations are on the left (toward lower values) skewed left : left side extends farther than right side most observations are on the right (toward higher values) NOTE: some distributions have shapes that are neither symmetric or skewed Peaks: which values are most common distributions can have few or many peaks
Unusual Features Gaps : areas of a distribution where there are no observations Outliers : extreme values that differ greatly from the other observations
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