DescriptionBasic Statistical Methods focuses on the fundamentals of statistics. It is designed to give professionals the means to efficiently and effectively summarize, analyze and interpret data. This course is beneficial to those in fields that involve the analysis of statistical information.
Lesson 1: The Nature of Statistics
- Describe the difference between descriptive statistics and inferential statistics
- Differentiate between a population and a sample
- Define the terms "variable" and "data"
- Describe the difference between qualitative and quantitative variables and data
- Describe the difference between discrete and continuous variables and data
- Define the four levels of data measurement
- Explain the role of statistics in everyday life
Lesson 2: Tabular and Graphical Methods Part I
- Construct and interpret summarization procedures for qualitative data, including frequency distributions, relative frequency, percent frequency distributions, bar graphs and pie charts
- Determine how to choose the best graphs/charts for qualitative data
- Construct and interpret summarization procedures for quantitative data, including stem-and-leaf displays, frequency distributions, relative frequency, percent frequency distributions, bar graphs, pie charts and line charts
Lesson 3: Tabular and Graphical Methods Part II
- Construct and interpret summarization procedures for quantitative data such as cumulative frequency distribution, cumulative relative frequency distribution, cumulative percent frequency distribution, histograms, frequency polygons, ogives, dot plots, box plots, scatter diagrams and time plots
- Construct and interpret summarization procedures for grouped data and bivariate data
Lesson 4: Describing Data Part I
- Explain the purpose of a measure of central tendency, compute and interpret the mean, trimmed mean, weighted mean, median and mode for a data set, and choose which to use in a given situation
- Discuss the advantages and disadvantages of using the mean, median and mode as measures of central tendency
- Explain the purpose of a measure of position, then define, compute and interpret the quantiles, percentiles, quartiles, quintiles and deciles for a data set
- Define, compute and interpret a proportion and a percentage for a data set
- Explain the purpose of a measure of variation, and compute and interpret the range, interquartile range, variance and standard deviation for a data set
- Distinguish between the formulas for the population variance and sample variance
- Define degrees of freedom
Lesson 5: Describing Data Part II
- Explain the purpose of the coefficient of correlation, and derive this measure for a data set
- Explain the importance of measures of shape, and identify whether a distribution is skewed and its kurtosis based on these measures
- Apply some practical uses of the mean and standard deviation, including the use of Chebyshev’s theorem and the empirical rule
- Learn how to compute the mean, median, variance and standard deviation from grouped data
- Apply exploratory data-analysis techniques such as 5-number summaries and box plots
- Use a box plot to identify outliers and to describe the probable shape of the distribution of a data set
Lesson 6: Basic Probability Part I
- Define the basic probability terminology: set, empty set, universal set, experiment, outcome, Venn diagram, tree diagram, sample space, probability and event, and use a Venn diagram and a tree diagram to represent events
- Differentiate between classical, relative and subjective probabilities
- Understand the meaning of odds
- Differentiate between joint, marginal and conditional probabilities, and calculate them from a contingency table
- Differentiate between independent and dependent events and exclusive and non-exclusive events
- Calculate the probability of an event from its experimental outcomes
Lesson 7: Basic Probability Part II
- Use the Addition Rule to calculate probability of both mutually exclusive and non-mutually exclusive events
- Use the multiplication rule to calculate the probability of both successive and simultaneous events
- Use the conditional probability formula
- Understand the purpose and use of permutations and combinations
- Calculate the probability of repeated trials
Lesson 8: Discrete Random Variables and their Probability Distributions
- Define randomness and describe the probability distribution of a discrete random variable
- Understand the conditions under which the binomial distribution may be used
- Use the binomial formula to determine probabilities
- Find the mean, variance and standard deviation of a binomial distribution
- Approximate the binomial distribution using the Poisson distribution
Lesson 9: Continuous Random Variables and their Probability Distributions
- Define the term continuous random variable
- Calculate the area under the probability distribution of a continuous random variable
- Describe the properties of a normal curve
- Calculate probabilities using the standard normal distribution
Lesson 10: General Concept of Hypothesis Testing
- Determine confidence intervals for situations where the population mean and standard deviation are both known and unknown
- Identify the null and the alternative hypotheses and how they relate to Type I and Type II errors
- Know whether to use a one-tailed or two tailed test
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