Learning Goal:Learning Goal: vDefine Statistics and understand its applications in the real world. vDifferentiate between Inferential & Descriptive Statistics. vDifferentiate between a parameter and a statistic.
StatisticsStatistics vThe science of collecting, analyzing, and drawing conclusions from data. vWhere do we encounter statistics in every day life? vWhy are they important? vAssignment: Statistics Artifact
Descriptive StatisticsDescriptive Statistics vThe methods of organizing and summarizing data. Collect and present data through graphical and numerical methods. Look for patterns in data and summarize. vExamples: vTake a poll, present the results. vA certain high school’s graduation rate vMrs. Lowery’s class data
Inferential StatisticsInferential Statistics vInvolves making generalizations from a sample to a population. vCollect data, generalize results to whole population by making an inference. vExamples: v2/3 of all high school student engage in underage drinking vOne in five adults have a sexually transmitted disease
PopulationPopulation vThe entire collection of individuals or objects being studied.
SampleSample vA subset of the population. vUsed to draw conclusions (make inferences) about the general population. Example: I want to study high school students study habits. Population: All high school students Sample: 500 high school students at BCHS
VariableVariable vAny characteristic whose value may change/vary from one individual to another. vWhat we are studying! vExamples: vSAT scores of students vDiameters of tires vParty affiliations of voters vSizes of T-shirts
Parameter vs. StatisticParameter vs. Statistic vParameter: A numerical value that summarizes the entire population. It a true value! vStatistic: A numerical value that summarizes the sample. True for the sample only! vExample: v40% of all BC students are on free/reduced lunch. 40% is a parameter. vChoose 200 students and find that 38% are on free/reduced lunch. 38% is a statistic.
Why do we sample?Why do we sample? vBrainstorm!!! vGet into your groups and give an example where we would want to sample rather than survey the entire population.
DataData vObservations of a variable of interest. vMeasurements
ExperimentExperiment vHow we collect data vPlanned activity to yield a set of data
ExampleExample vA statistics student is interested in finding out something about the average dollar value of cars owned by the faculty members of Brookland-Cayce High School. Each of the terms described can be identified in this situation. 1. Population: the collection of cars owned by all BCHS faculty members. 2. Sample: any subset of that population. For example, the cars owned by the mathematics department is a sample. Can you give me another example? 3. Variable: the dollar value of each individual car. 4.Data: are the set of values associated with the sample we obtained. For example, Ms. Cox’s car is worth $15,000, so it is a data value within our data set. 5. Experiment: consists of the methods used to select the cars that form the sample and to determine the value of each car in the sample. It could be carried out by questioning each member of the mathematics department, or in other ways. 6. Parameter: about which we are seeking information is the average value of all cars of BCHS faculty. 7. Statistic: that will be found is the average value of the cars in the sample.
Discuss… Discuss… vNow, what if a seconds sample were taken? Would we still have the same statistic? What if we sample all the administrators or say, the English department?
Article JigsawArticle Jigsaw vGet into your groups and share your articles. On a separate sheet of paper try to identify the following for each article: vPopulation vSample vExperiment vVariable vData vStatistic vParameter vYou may not be able to identify all of these!
Categorical VariablesCategorical Variables vCan be called qualitative or categorical. vIdentifies basic differentiating characteristics of the population. vExamples: vHair color vEye color vFavorite music
Numerical VariablesNumerical Variables vCan be called quantitative or numerical. vObservations or measurements that take numerical values. vRULE OF THUMB: Does it make sense to average the number? vExamples: vNumber of students in Mrs. Lowery’s classes vHigh school graduation rate
PracticePractice 1.Income of Columbia households NUMERICAL 2.Color of M&M candies CATEGORICAL 3.Number of speeding tickets this class has had NUMERICAL 4.Area codes in South and North Carolina CATEGORICAL
Numerical VariablesNumerical Variables vCan be divided into 2 groups: vDiscrete vContinuous Variables Numerical Categorical Discrete Continuous
Discrete VariablesDiscrete Variables vCan be counted vHave gaps between values vExamples: vNumber of students in classes at BC vShoe size
Continuous VariablesContinuous Variables vCan assume any value along a range of numbers. vAre often measurements of things. vCannot be counted! vExamples: vTemperature vHeight
PracticePractice 1.Weights of fire fighters CONTINUOUS 2.Flip 4 coins and count the number of heads DISCRETE 3.Number of football players with head injuries DISCRETE 4.Length of snakes in the Riverbanks Zoo reptile house CONTINUOUS
Levels of Measurementv4 Levels of Measurement for Variables 1. Nominal 2. Ordinal 3. Interval 4. Ratio vRatio is the highest level of measurement Levels of Measurement
Nominal LevelNominal Level vThe prefix NOM in Latin means Name vThis level of measurement classifies data into mutually exclusive categories where no order or ranking can be imposed! vCan NOT be ranked!!!!!
Ordinal LevelOrdinal Level vThe prefix ORD stands for Order vThis level of measurement classifies data into categories that CAN be ranked!
Interval LevelInterval Level vThis level of measurement is used to classify data that is numerical and has no true zero. vNo true zero means that it can take negative values (Zero does not mean anything!) vExample: vTemperature
Ratio LevelRatio Level vThis level of measurement is used to classify data that is numerical and HAS a true zero. vDoes not take negative values, and zero is the absolute bottom! vHint: If it is not Ratio, it is Interval, and vise versa!
Questions to ask yourself…Questions to ask yourself… Is it a number or a category? Number Category Can it be negative? YES NO INTERVAL RATIO Can I rank it? YES NO ORDINAL NOMINAL
PracticePractice vZip Code NOMINAL vGrade (A, B, C, D, F) ORDINAL vTime RATIO vWeight RATIO vTemperature INTERVAL vNCAA Basketball Rankings ORDINAL vNationality NOMINAL vPolitical Affiliation NOMINAL vAge RATIO vSalaries RATIO