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

(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

(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

➢ 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.

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. 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 1 2 3 How to construct a stemplot 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) 2. Write the stems vertically in increasing order from top to bottom, and draw a vertical line to the right of the stems. 3. Go through the data, writing each leaf to the right of its stem in increasing order. 4. Title your graph and add a key describing what the stems and leaves represent. NOTE: Depending on the data we may need to create a split stemplot or round our data before making a stemplot.

Spread:

Center:

Shape:

Peaks:

Spread: 15 - 47

Center: 28

Shape: bell-shaped

Peaks: 20-29 Laps Swum by Britney in 30 Days

Stem (Split-Stemplot) Leaf Laps Swum by Britney in 30 Days

Spread:

Center:

Shape:

Peaks: Back-to-Back Stemplots

➢ 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. •This back-to-back stemplot shows the amount of cash (in dollars) carried by a random sample of teenage boys and girls. •The boys carried more cash than the girls - a median of $42 for the boys versus $36 for the girls. •Both distributions were roughly symmetric. Ages of Actors and Actresses

when they Won an Oscar

ACTORS ACTRESSES

2 1 4 6 6 6 7

9 9 8 7 5 3 2 2 1 3 0 0 1 1 3 3 4 4 4 5 5 7 7 8

8 8 7 6 5 4 3 3 2 2 1 0 0 4 1 1 1 2 9 Spread: 6 6 5 1 5 Center: 2 1 0 6 0 1 1

Shape: 6 7 4

Peaks: 8 0

KEY: 3 2 = 32 yrs old Ages of Actors and Actresses

when they Won an Oscar

ACTRESSES ACTORS

7 6 6 6 4 1 2

8 7 7 5 5 4 4 4 3 3 1 1 0 0 3 1 2 2 3 5 7 8 9 9

9 2 1 1 1 4 0 0 1 2 2 3 3 4 5 6 7 8 8

5 1 5 6 6

1 1 0 6 0 1 2

4 7 6

0 8

KEY: 3 2 = 32 yrs old Dotplots ➢ 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

0 1 2 3 4 5 6 7 Histograms

➢Write down your height in inches.

➢Collect all data on the whiteboard.

➢Create a histogram.

➢Describe graph ●Shape, spread, peak, median, mean,

mode