Statistics and ModelsStatistics and Models

Ch. 2 Sec. 2Ch. 2 Sec. 2

Using StatisticsUsing Statistics

►Statistics = collection and Statistics = collection and classification of data that are in the classification of data that are in the form of numbers.form of numbers.

Summarize, characterize, analyze, and Summarize, characterize, analyze, and compare datacompare data

Georgia

   Further information

    People MapStats Georgia USA

   Population, 2008 estimate 9,685,744 304,059,724

   Population estimates base (April 1) 2000 8,186,812 281,424,602

   Population, percent change, April 1, 2000 to July 1, 2008 18.3% 8.0%

   Population, change, April 1, 2000 to July 1, 2008 1,498,932 22,635,122

   Persons under 5 years old, 2007 737,422 20,724,125

   Persons under 5 years old, percent, 2007 7.7% 6.9%

   Persons under 18 years old, 2007 2,531,609 73,901,733

   Persons under 18 years old, percent, 2007 26.5% 24.5%

   Persons 65 years old and over, percent, 2007 9.9% 12.6%

   Persons 65 years old and over, 2007 942,832 37,887,958

   Female persons, percent, 2007 50.8% 50.7%

 

Statistics and PopulationStatistics and Population

►Statistical population = group of Statistical population = group of similar things that a scientist is similar things that a scientist is interested in learning aboutinterested in learning about

Enrollment information for Model High School

AverageAverage

►Average = meanAverage = mean Mean = the number obtained by adding Mean = the number obtained by adding

the data for a characteristic and dividing the data for a characteristic and dividing this sum by the # of individualsthis sum by the # of individuals

Six students scored 72, 75, 78, 82, 84, and 92 on a test. To calculate the average, add 72 + 75 + 78 + 82 + 84 + 92 and divide the sum (483) by six. The average score would be 80.5.

DistributionDistribution

►Distribution = relative arrangement of Distribution = relative arrangement of the members of a statistical population the members of a statistical population Pattern the bars createPattern the bars create

DistributionDistribution

►Normal Distribution = bell-shaped Normal Distribution = bell-shaped curve curve Group symmetrically around the meanGroup symmetrically around the mean

ProbabilityProbability

►Probability= the chance that Probability= the chance that something will happensomething will happen

Odds of winning an Olympic medal: 662,000 to 1

Odds of injury from shaving: 6,585 to 1

Odds of being struck by lightning: 576,000 to 1

ProbabilityProbability

►Sample size = number of objects or Sample size = number of objects or events sampledevents sampled Must represent population (can’t be too Must represent population (can’t be too

small or too big)small or too big)

RiskRisk

►Risk = the probability of an unwanted Risk = the probability of an unwanted outcomeoutcome

ModelsModels

► Models = representations of objects Models = representations of objects or systemsor systems

1.1. PhysicalPhysical

2.2. GraphicalGraphical

3.3. ConceptualConceptual

4.4. MathematicalMathematical

Physical ModelsPhysical Models

►3-D models you can touch and closely 3-D models you can touch and closely resemble what they representresemble what they represent DNA, Globe, Cell, DNA, Globe, Cell,

Graphical ModelsGraphical Models

►Maps and chartsMaps and charts Position of stars, amount of forest, depth Position of stars, amount of forest, depth

of waterof water

Conceptual ModelsConceptual Models

►Verbal or graphical explanation of how Verbal or graphical explanation of how a system works or is organizeda system works or is organized Flow chart, diagramsFlow chart, diagrams

Mathematical ModelsMathematical Models

►One or more equations that represents One or more equations that represents the way a system or process worksthe way a system or process works Lots of variablesLots of variables

cube = a 3             rectangular prism = a b c             irregular prism = b h             cylinder = b h = pi r 2 h             pyramid = (1/3) b h             cone = (1/3) b h = 1/3 pi r 2 h             sphere = (4/3) pi r 3             ellipsoid = (4/3) pi r1 r2 r3