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STAT 301 (55)
Lecture

# Measure of center, measure of spread, variance, standard deviation, interquartile range, boxplots

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School
Department
Statistics
Course
STAT 301
Professor
Brett Hunter
Semester
Fall

Description
24 August A parameter is a value that pertains to the population Denoted by a Greek letter A statistic is a value that pertains to a sample Denoted by a Roman letter Numbers to describe data Measure of center For numeric variables: x Mean (μ for parameter, for statistic) Median Mode ≈ ≈ If histogram is symmetric, mean median mode If histogram is right skewed, mean > median > mode If histogram is left skewed, mean < median < mode For categorical variables: proportion of “successes” ̂ p π for parameter; , p, for statistic Still need to find a measure of spread, as just knowing where the center of the data is does not give us all the information we need. Measures of spread – provides a measure of uncertainty Range = max – min Deviation from sample mean How far a particular observation is from the sample mean X - x i Xi= the ith value from data set Measure of spread would need to include all deviations n ∑ (x −́ )0 Can’t take average of deviations, as i=1 i Say x = 3, x = 4, x = 6 1 2 3 3 ∑ xi = 3 + 4 + 6 i=1 Σ indicates a summation Variance Average squared deviation from the mean n 2 ∑ (x1−́x)2 S = i=1
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