MTH 2030 Module 1
1. Statistical Data Collection for Representative Sampling
○ A representative sample is one where the individuals in the
sample reflect the properties of an entire population17.
○ The demographic characteristics of the individuals in the sample
must be similar to those in the population: gender, rural, urban,
religion, marital status, income levels, etc17.
○ There are many methods used to collect or obtain data for
statistical analysis. Three of the most popular methods are: Direct
Observation, Experiments, and Surveys21.
○ In simple random sampling (SRS), researchers take a complete list
of the population and randomly select participants from it. All
population members have an equal likelihood of being selected 20.
2. Measuring Central Tendency, Dispersion, and Position
○ Central Tendency: Measures of central tendency include
arithmetic mean, median, and mode3.
○ Dispersion: The most common measure of variation, or spread, is
the standard deviation28.
○ Position: This can be determined using percentiles or quartiles,
which divide the data into equal parts.
3. Calculating the Probability of Simple and Compound Events
○ Simple Event: The probability of a simple event is given by the
number of favorable outcomes divided by the total number of
outcomes6.
○ Compound Event: The compound probability of compound
events can be defined as the likelihood of occurrence of two or
more independent events together5. The formulas to calculate the
compound probability are different for mutually exclusive and
mutually inclusive events5.
4. Difference Between Discrete and Continuous Probability
Distributions
MTH 2030 Module 1
○ A discrete distribution is one in which the data can only take on
certain values, for example integers9.
○ A continuous distribution is one in which data can take on any
value within a specified range (which may be infinite)9.
5. Calculating the Probability for Discrete and Continuous Variables
○ Discrete Variables: A binomial distribution is a discrete probability
distribution that gives the success probability in n Bernoulli trials 26.
○ Continuous Variables: The probability density function is used to
calculate probabilities for continuous variables22.
6. Determining Measures of Center, Spread, and Position
○ Center: The two most widely used measures of the center of the
data are the mean (average) and the median27.
○ Spread: The most common measure of variation, or spread, is the
standard deviation28.
○ Position: This can be determined using percentiles or quartiles,
which divide the data into equal parts.
7. Addition and Subtraction Rules for Probability Theory and
Distributions
○ Addition Rule: For any two events A and B, the probability of A or
B is the sum of the probability of A and the probability of B minus
the shared probability of both A and B14.
○ Subtraction Rule: The probability that event A will occur is equal
to 1 minus the probability that event A will not occur15..
Source(s)
1. Representative Sample: Definition, Uses & Methods - Statistics by Jim
2. Data Collection and Sampling - University of Texas at Dallas
3. Sampling Methods: Different Types in Research - Statistics by Jim
4. Measure of Central Tendency of Group Data - ClassNotes.ng
5. 2.3.2: Measures of Center and Spread Part 2 - Statistics LibreTexts
6. What are Simple and Compound Events in Probability?
7. Compound Probability - Formulas, Definition, Examples - Cuemath
8. Continuous vs. Discrete Distributions - Statistics.com: Data Science ...
9. Discrete Probability Distribution - Examples, Definition, Types - Cuemath
10. Probability Distribution | Formula, Types, & Examples - Scribbr
MTH 2030 Module 1
11. 2.3.1: Measures of Center and Spread Part 1 - Statistics LibreTexts
12. Addition Rules in Probability and Statistics - ThoughtCo
13. Rules of Probability - stattrek.com
14. Lesson 1: Measures of Central Tendency, Dispersion and Association
15. 8.1: Measures of Central Tendency and Dispersion (Ungrouped Data)
16. Measures of Central Tendency - Formula, Meaning, Examples - Cuemath
17. Compound events - Math.net
18. Discrete vs Continuous Probability Distributions
19. What is the difference between a discrete and continuous probability ...
20. What is the difference between discrete probability distribution and ...
21. 4.3: The Addition and Multiplication Rules of Probability
22. 7.9: The Addition Rule for Probability - Mathematics LibreTexts
23. Addition Law of Probability - ProofWiki
24. Sampling Methods | Types, Techniques & Examples - Scribbr
25. Statistics: Basic Concepts: What is Sampling? - GCFGlobal.org
26. Poisson Distributions | Definition, Formula & Examples - Scribbr
27. 5.1: Discrete versus Continuous Distributions
28. Probability Distributions: Discrete and Continuous - Medium
29. Shape, Center, and Spread of a Distribution - Emory University
30. Center and spread | Lesson (article) | Khan Academy
31. 3.1: Measures of Center - Statistics LibreTexts
32. en.wikipedia.org