Final exam is comprehensive and includes all materials
covered in this term.
For details, please refer to the class notes distributed
Lecture 1. Introduction
Statistics-population-parameter-sample-statistic
Data classification:
Qualitative-quantitative
Discrete-continuous
Level of measurement: nominal-ordinal-interval-ratio
Lecture 2.Frequency distributions
Frequency distribution: class frequency, class midpoint, class interval
Relative frequency
Cumulative frequency
Tabular form: how to develop a frequency distribution table-five-step procedure
Graphical form for quantitative:
Histogram: frequency, relative, and cumulative
Polygon: frequency, relative, and cumulative
Graphical form for qualitative
Bar chart:
Pie chart
Represent medium size data without loss of information
Stem-and-leaf
Lecture 3. Measure of Central Tendency
Mean:
Arithmetic mean and weighted mean
Raw data
Grouped data
Geometric mean
Median
Raw data
Grouped data
Mode
Raw data
Grouped data
Lecture 4. Measure of Dispersion (no calculation on skewness, Kurtosis, correlation)
Range
Raw data
Grouped data
Mean absolute deviation
Population
Sample
Variance and standard deviation
Raw data
 fx

2
Grouped data:  
Population:  
Sample:  
 f ( x  x)
n 1
 (x  )
2

 fx
2
n 1
n
2
n
 ( x  x)
2
n 1
Conceptual formula
Computational formula
Cehbyshev’s Theorem
Empirical rule (68, 95, 99.7)
Compare more than one data set with different units or one data set with
widespread mean:
Coefficient of variation
Population: CV 
Sample: CV 


x
Lecture 5. Probability
Random experiment


Outcome
Sample space
Event
Probability
Venn diagram
Tree diagram
Mutually exclusive events
Exhaustive events
Impendent of events
Rule of probability
Addition: special and general
Multiplication: special and general
Complement
Conditional probability
Joint Probability vs marginal probability
Total probability formula
Bayes’ theorem
Rule of counting
Multiplication
Combination
Permutation
Chapter 6. Random variables
Random variable
Discrete
Continuous
Probability distribution
Tabular
Graphical
Formula
Joint and marginal probability distribution
Function of r.v’s is again a r.v
Contingency table
Independence of r.v’s
Expectation
Definition
Rule of expect ion
Variance and standard deviation
Definition
Rule of variance
Bernoulli and Binomial
The characteristics of Bernoulli and Binomial probability distribution
Expectation and variance of Binomial and Bernoulli random variable
Calculate probability for Binomial distribution using the Binomial Table
Chapter 7. Normal distribution
The characteristics of a standard/general normal probability distribution
Calculate probability in a given interval for standard/general normal and
probability distribution using the standard normal table, and vice versa.
Lecture 8. Sampling Technique
SRR
Central limit theorem
Lecture 9. Estimation
Point estimator
Unbiasedness
Interval estimation
Level of confidence
Margin of error
Construct a confidence interval for the population mean:
(1   ) -confidence interval for population mean 
( X  z / 2 / n , X  z / 2 / n )
The formula above can be used only under one of the following conditions:
(1) Sample size n is at least 30 (if  is unknown, use sample standard deviation s)
(2) Sample size n is smaller than 30, but  is known, and the population is
normally distributed
Select an appropriate size for given level of confidence and margin of error
Lecture 10
Hypothesis
Hypothesis Testing (Two-tailed or one-tailed)
Type I, II errors
Level of significance
Five-step procedure for testing 
p-value