Review for Exam 1

Describing Univariate Data

• Numerical Summaries

  • Measuring Location (Center)

    Three most commonly used measure of center: mean, median and mode.
    Percentiles. Quartiles (1st quartile = Q1, 3rd quartile = Q3).
    Extremes: minimum and maximum.
    The median, upper and lower quartiles, minimum and maximum are collectively called the five-number summary.
    Z-score: How to compute it? What does it mean?
    

  • Measuring Scale (Spread)

    Most commonly used: variance, standard deviation (square-root of variance), inter-quartile range (IQR), range (max-min).
    

  • Properties

    Shapes of distribution: symmetric, skewed left or skewed-right.
    Unimodal: has a single peak.
    Tails: long tailed (many outliers) or short tailed (few outliers).
    When are median and IQR preferable to mean and variance: outliers present, or distribution skewed.
    Empirical Rule: what does it say? What assumption(s) do you need to use it?
    Chebychev's Rule: what does it say? What assumption(s) do you need to use it?
    

• Graphical Summary

  Stem-and-leaf display: How to construct it? What does it show? Advantages and disadvantages?
  Histogram: What does it show? Advantages and disadvantages?
  Boxplot: How to construct it? What does it show? Advantages and disadvantages?
  Normal quantile plot: What does it show?
  

Bivariate Data

Numerical Summaries:
Pearson's correlation coefficient: what does it measure? when is it applicable? what values can it take on?
Spearman's rank correlation coefficient: what is it? why use it?
Least Squares line: what is it? what's the relationship with correlation coefficient? what does the intercept and slope mean?
Coefficient of determination: What is it? what does it mean? what values can it take on?
Graphical Summaries: scatterplot.

Basic Probability

• Basic Definitions

  Definition (or meaning of) sample space, event, random experiment, union, intersection, complement, mutually exclusive, random variable, expected value.
  The three basic rule of probability.
  Conditional probability: what does it mean?
  The difference between mutually exclusive and independent.
  

• Discrete Distributions

  What are the situations/setup for the following distributions: binomial, hypergeometric, negative binomial, Poisson.
  The difference between sampling with and without replacement.

Normal Distribution, Sampling Distribution of a Statistic

• Normal distribution

  How does a generic normal distribution relate to the standard normal distribution?
  

• Sampling Distributions

  Definitions: population, random sample, parameter, statistic, sampling distributions.
  Basic situations for statistical inference: what are the parameters and corresponding statistics?
  Sampling from one, two or several continuous populations.
  Sampling from one, two or several 0-1 populations.
  Paired data.
  Simple linear regression and correlation.

• Central Limit Theorem

  What does it say? What does it assume?
  Normal approximation to the binomial probabilities: an application of the CLT.

• Transformed Statistics

  A transformed statistic measures how close a statistic is to the corresponding parameter. The sampling distribution of a transformed statistic tells us how likely for a random sample to yield a statistic with the value we got from our particular sample.

  
  

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