Stat 160 Midterm Review
Chapter 1 – Descriptive Statistics
§ Shapes of Distributions
o Symmetric, asymmetric, right skewed, left skewed, etc.
§ Five Number Summary
o (Min,Q1,Med,Q3,Max)
o Boxplots
o Identifying outliers (LIF and UIF)
§ Other Statistics
o Measures of Center
§ Sample Median* - Q2
§ Sample Mean* -
§ HL Estimate*
o Measures of Scale
§ Range*
§ IQR* = Q3 – Q1
§ Sample Variance/Standard Deviaiton – s2/s
§ Linear Relationships
o Prediction Equation -
o Meaning of the intercept and the slope
o Residuals -
o Correlation Coefficient – r
o Coefficient of Determination – R2
o Determination of a good model
§ Robust Statistics
o Which of the statistics given above are robust?
Chapter 2 - Probability
§ Tree Diagrams
§ Sampling with replacement OR without replacement.
§ Relative Frequency -
§ Independence
o P(B|A) = P(B) i.e. event B does NOT depend on event A.
§ Useful Formulas
o In general, P(A and B) = P(B|A)P(A) = P(A|B)P(B)
o If A and B are independent, P(A and B) = P(A)P(B)
o Complement – P(AC) = 1 – P(A)
Chapter 3 – Resampling/Simulation
§ Experiment
o Trials of the experiment are independent and taken under identical conditions.
o , A-Event of Interest and N – Number of Trials
o Error =
o Setting up the correct model (GA#7)
§ (Number of Trials, Min Value, Max Value, Number Drawn, with replacement or without replacement)
Chapter 4 – Probability Models for Discrete Distributions
§ Probability Model
o Mean - for all values in the Range of X
o Variance - for all values in the Range of X
§ Binomial Distribution
o X is the # of Successes out of n trials with P(S) = p.
o X is Bin(n,p). Range of X is {0,1,2,…,n}
o Mean -
o Variance -
o pbinom(k,n,p). P(of at most k successes)
o P(X = k) = dbinom(k,n,p). P(exactly k successes)
§ Poisson Distribution
o X is a count over some time interval. The average occurrence over that interval is .
o If 2 intervals do NOT overlap then the occurrence of events in these intervals are independent.
o X is POI(). Range of X = {0,1,2,…}
o ppois(k,n,p). P(of at most k)
o P(X = k) = dpois(k,n,p). P(exactly k)
Chapter 5 – Probability Models for Continuous Distributions
§ Uniform Distribution
§ Normal Distribution
o Symmetric bell-shaped curve (i.e. median = mean)
o X is N(m,s2) – Mean = m, Variance = s2
o P(X<k) = pnorm(k,m,s). Note: 3rd input is standard deviation NOT variance.
o P(X>k) = 1 - pnorm(k,m,s).
o P(a<X<b) = pnorm(b, m,s) - pnorm(a, m,s).
Chapter 6 – Central Limit Thoerem
§ If X is a random variable from some distribution with mean, m, and variance, s2, then the sample mean () of a random sample of size, n, is
§ Apply Chapter 5 to solve probability problems based on the normality of .