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
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
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 )
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
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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