Chapter 1, Chapter 2 (Section 2.1) Quiz Review Terms Individuals: - - PowerPoint PPT Presentation
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 .
➢Individuals: objects described by a set of data. ➢Variable: any characteristic of these individuals
groups or categories.
which arithmetic operations such as adding and averaging makes sense.
➢Is Calculator number categorical or quantitative variable? ➢Is Test 1 categorical or quantitative?
Name Sex Homeroom Grade Calculator # Test 1 Danny M
Senior B319 81 Francine F
Senior B298 92 Ricardo M
Junior B304 87
Player Team Votes Points per Game Height (inches) Position 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?
Player Team Votes Points per Game Height (inches) Position 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
Player Team Votes Points per Game Height (inches) Position 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?
Player Team Votes Points per Game Height (inches) Position 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
Player Team Votes Points per Game Height (inches) Position 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
Player Team Votes Points per Game Height (inches) Position 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?
➢ 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)
entire population
➢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.
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?
(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.
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. I. Analyze data: Graphs and numerical summaries are the tools for describing patterns in the data, as well as any deviations from those patterns. I. Interpret results: The results of the data analysis should help answer the question of interest.
➢ Bar graph and Pie Chart: good for
➢ Histograms, Dot Plots, Time Plots, and
➢ Histograms ➢ Dot Plots
➢ Time Plots: plots each observation
➢ Ogives
We interpret a graph by describing the:
Spread: _____________________________________________________ Center: _____________________________________________________ Also known as the ____________
We interpret a graph by describing the:
Spread: the range, lowest and highest values Center: point where half the observations are above and half are below (median)
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
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
1. Separate each observation into a stem, consisting of all but the rightmost digit and, a leaf, the final digit. (4 stems is a good minimum)
and draw a vertical line to the right of the stems.
increasing order.
leaves represent. NOTE: Depending on the data we may need to create a split stemplot
Stem (Split-Stemplot) Leaf
Spread: Center: Shape: Peaks:
➢ Compares data from two populations. ➢ The center of a back-to-back stemplot consists of a column of stems, with a vertical line on each side. ➢ Leaves representing one data set extend from the right, and leaves representing the other data set extend from the left.
stemplot shows the amount
by a random sample of teenage boys and girls.
cash than the girls - a median of $42 for the boys versus $36 for the girls.
roughly symmetric.
Spread: Center: Shape: Peaks:
➢ Label horizontal axis starting with minimum value in data through largest data entry ➢ For each occurrence of the value, place a dot above the corresponding value. ➢ Dots should be equal sized
1 2 3 4 5 6 7
Histograms