Grant MacEwan University
STAT 151 – Formula Sheet – Final Exam
Dr. Karen Buro
Descriptive Statistics
•Sample Variance: s2=Pn
i=1(xi−¯x)2
n−1=Σn
i=1x2
i−(Σn
i=1xi)2
n
n−1
•Sample Standard Deviation: s=√Sample Variance = √s2
•Median: Order the data from smallest to largest. The median Mis either the unique
middle value or the mean of the two middle values.
•Lower Quartile: Order the data from smallest to largest. The lower quartile Q1is the
median of the smaller half of the values.
•Upper Quartile: Order the data from smallest to largest. The upper quartile Q3is the
median of the upper half of the values.
•Interquartile Range (iqr) = Upper Quartile – Lower Quartile =Q3−Q1
•Outliers: lower fence =Q1−1.5iqr and upper fence=Q3+ 1.5iqr
Probability Theory
•Addition Rule: P(Aor B) = P(A) + P(B)−P(A&B)
•Complement Rule: P(A does not occur) = P(not A) = 1 −P(A)
•Multiplication Rule: P(A&B) = P(A|B)P(B)
•Multiplication Rule for Independent Events:
If A and B are independent, then P(A&B) = P(A)P(B)
•Conditional Probability of Agiven B, if P(B)>0 : P(A|B) = P(A&B)
P(B)
Population Distributions
•The mean (expected value) of a discrete random variable: µ=Pxp(x).
•The variance of a discrete random variable: σ2=X(x−µ)2p(x)
•The standard deviation of a discrete random variable: σ=√σ2
Binomial Distribution
•Probability to observe ksuccesses in ntrials: p(k) = P(x=k) = ³n
k´pk(1 −p)n−k
•³n
k´=n!
k!(n−k)!
•Mean and standard deviation of a binomial distribution: µ=np and σ=qnp(1 −p)
