Contact information - Department of Statistical Science联系信息-统计科学系.pptVIP

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Contact information - Department of Statistical Science联系信息-统计科学系.ppt

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Contact information - Department of Statistical Science联系信息-统计科学系

Intro to statistics Continued Grading policy Quizzes (and relevant lab exercises): 20% Midterm exams (2): 25% each Final exam: 30% Cutoffs based on final avgs (A, B, C): 91-100, 82-90, 73-81 Numerical descriptions Measures of central tendency “Where’s the middle of the data?” Two major ones are mean and median Measures of dispersion “How much variation is there in the data?” Major ones are variance, standard deviation, and inter-quartile range (IQR) Mean Sum data points and divide by number of data points (the average) Provides “balance point” of data Easily influenced by outliers Easy to calculate and interpret for audiences Population mean: μ, sample mean: Median Sort data points, median is the middle data point (interpolate between the middle two data points if the number of data points is even) Not very susceptible to outliers Not as easy to interpret for audiences, often less useful mathematically Percentiles Median: 50th percentile, boundary value separating bottom and top halves of population xth percentile separates the bottom x% from the top (100-x)% First quartile (Q1): 25th percentile (marks boundary for lower 4th) Third quartile (Q3): 75th percentile (marks boundary for upper 4th) Variance Might want to measure dispersion as avg distance of each data point from the mean as But this is always 0, so look at the avg squared distance Standard deviation is sq root of variance Sample variance differs in minor ways; more about uses for this later Variance (cont.) Pros Mathematically useful Frequently used More understandable to audiences Cons Easily influenced by outliers Difficult to calculate by hand Inter-quartile range Also called IQR, is Q3 – Q1 “How far is the median of the top half from the median of the bottom half?” Not as susceptible to outliers as the variance Not as commonly used by general audiences Population variance Requires knowing μ (mean of population): This if fine if we know about all the members of a population (so we can know the