Review for Exam 1
Describing Univariate Data
Type of data: categorical vs. numerical, continuous vs. discrete.

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 fivenumber summary.
Zscore: How to compute it? What does it mean?

Measuring Scale (Spread)
Most commonly used: variance, standard deviation (squareroot of
variance), interquartile range (IQR), range (maxmin).

Properties
Shapes of distribution: symmetric, skewed left or skewedright.
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
Stemandleaf 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 01 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.