Week 2 -- Central Tendency

Week 2 -- Central Tendency - Numerical Descriptive...

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Numerical Descriptive statistics The use of numbers (as opposed to graphs) for describing (or “summarizing”) properties of the sample
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Numerical Data Properties or how can we “summarize” the properties of a sample? Central Tendency (Location) Variation (Dispersion) Shape Frequency Frequency Age Age Age Age Age Age
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Numerical Data Numerical Data Properties Mean Median Mode Central Tendency Range Variance Standard Deviation Variation Percentiles Relative Standing Interquartile Range Z–scores
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NUMERICAL NUMERICAL DESCRIPTIVE STATISTICS DESCRIPTIVE STATISTICS Measures of Central Tendency Measures of Central Tendency
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MEASURES OF CENTRAL TENDENCY The following are typical measures of central tendency for a population Mean -- the average Median -- the middle observation after the data has been ordered Mode -- the observation that occurs most often
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One measure of central tendency is the mean The population mean is the average (or weighted average) of all observations of the population Population mean for a population of size N: μ = Σ x i /N Population Mean ( μ )
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Mean 1. Measure of central tendency 2. Most common measure 3. Acts as ‘balance point’ 4. Affected by extreme values (‘outliers’) 5. Formula (sample mean) X X n X X X n i i n n = = + + + = 1 1 2
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Example N = 2000 students took an introductory stats class last year at CSUF. Using the 4- point scale (A=4, B=3, etc.) the following were the grades 4,2,1,3,3,3,2,… 2. The mean grade of all statistics students was: μ = (4+2+1+3+3+3+2+…+2)/2000 = 2.39
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Calculating μ Using Frequency Data A simpler description of the data Example A(4) = 304, B(3) = 530, C(2) = 852, D (1) = 270 F(0) = 44 μ = (304(4) +530(3) +852(2) +270(1) +44(0))/2000 = 2.39 Note the relative frequencies are found by dividing by N (which is
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Week 2 -- Central Tendency - Numerical Descriptive...

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