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STATS 2B03
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Aaron Childs
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Lecture

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Statistics

STATS 2B03

Aaron Childs

Fall

Description

Lecture 12January0713838 AM1214 Some TerminologyThe target populationconsists of all the subjects that are being studied ex Canadians mac studentsA sampleis a group of subjects selected from population Descriptive StatisticsCh 2 consists of summarizing and presenting data ex average marks of a test or a histogram of the marks Inferential StatisticsCh 6 on consists of using a sample to make a conclusion about a population using probabilityCh 35 ex taking a opinion poll of a sample of a population and making an inference of the whole population based on thatLarger samples lead to more accurate estimate of inferential statisticsThe sampled populationis the population from which the sample is drawnEx Sampled population depends on how you collect the sample if you were interested in Canadians but only chose from people in Hamilton Ex2 If I am interested in the average age of Mac Students then the target population is all Mac students If I take a sample of 30 students from class then the sampled population is everyone in this class This would be wrong to doIn order to use inferential statisticsthe sampled population should be the same as target population The sample should be randomly selected from the target population Quantitative Variables are variables that can be measured ex height weight age etc Qualitative Variables are characteristics that cannot be measured but can only be categorized ex gender eye colour raceScales of Measurementfor qualitative variables some qualitative variables that can be put in a order or ranking others cannot ex how much you exercise 3 categories often a few times neverThe nominalscale consist of categorizing observations by name only where the different categories cannot be ranked ex gender or race there is no order into these categoriesThe ordinalscale consists of categorizing observations in such a way that the different categories can be ranked according to same criterion ex income exercise not actually collecting or using the exact numbers but being able to place people in different ranks based on number23 Organizing DataCumulative frequency is useful in larger data sets as it can Example 55 63 72 41 87 75 64 60show you that 5 people got less than 70Frequency TableRelative Frequency is the percentage GroupingFrequency Cumulative FrequencyRelative FrequencyCumulative Percent405011125125506012 1112525607035 113375625708027 113225875809018 11321125100The groupings used ex 8090 are class boundariesConvention when the class boundaries overlap the right class boundary isnotincluded in the interval it ends up being 8089 essentially you could say 8089 but if you start using decimals it can get messyHistogram Inclass Notes Page 1 HistogramStem and Leaf Plots1 41Example 55 63 72 41 87 75 64 60grouping 4050 5060 etc2 55Median 63642635 3 6034 of observations in the row containing the median The first column shows the first number 4 in 40 5 in 503 725The second column only shows the ones 1 in 41 5 in 55The numbers from the data set example 1 87Definition the medianof an ordered data set with n observations is the middle value if n is odd and the average of the middle two values if n is even eg 58102125 n5 numbersMedian 10 eg 61215182671 n6Median15182165 Example Contd Grouping 4045 4550 5055 etc Example 28 29 30 32 54 67 69Leaf unit used to give you the original value Inclass Notes Page 2 Leaf unit can be negativeNote the median cannot be split between two different rows it is always one number and rows do not overlap since we use the conventional method24 Measures of Central TendenciesThe average of a sample x1 x2xn is called the sample meanor mean and is denoted by The average of the population xq x2 xN is called population meanand is denoted byCant calculate population mean but you can estimate since we dont have the actual populationNote that N is the population size n is the sample size The modeof a data set is the value that occurs most often eg 7888910 mode 8eg 7888999101011 mode 8 and 9In a grouped data set the modal class is the group with the largest frequency eg GroupingFrequency4050150601Modal class607037080280901 Inclass Notes Page 3

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