8. Probability and Statistics#
This chapter connects probability with descriptive statistics. You will use chance models, summaries, and sampling variation to reason about uncertain business outcomes.
Chapter Video
Video credit: CrashCourse. (2018, April 25). Probability Part 1: Rules and Patterns: Crash Course Statistics #13. YouTube. Watch on YouTube.
This embedded video is provided for educational reference only. All rights are retained by the respective copyright holder.
Learning Objectives
By the end of this chapter, you will be able to:
Describe a probability model and compute event probabilities, complements, and expected values.
Summarize a distribution by its center, spread, and shape.
Interpret empirical distributions in business contexts.
Explain why samples vary, and use simulation to show it.
Use the standard error to describe how sample size affects the precision of an estimate.
Chapter Flow
Glossary
# |
Term |
Explanation |
|---|---|---|
1 |
Probability |
A number between 0 and 1 describing how likely an event is. |
2 |
Event |
An outcome or set of outcomes of interest. |
3 |
Complement |
The event that a given event does not happen; P(not A) = 1 − P(A). |
4 |
Outcome |
A possible result of a random process. |
5 |
Sample space |
The collection of all possible outcomes. |
6 |
Chance model |
A simplified representation of a random process. |
7 |
Random variable |
A numeric quantity whose value depends on chance. |
8 |
Expected value |
The long-run average of a random variable: the sum of each value times its probability. |
9 |
Distribution |
The pattern of possible values and their probabilities or frequencies. |
10 |
Empirical distribution |
A distribution built from observed data. |
11 |
Law of large numbers |
As the number of observations grows, the sample average gets closer to the true average. |
12 |
Mean |
The arithmetic average of numeric values. |
13 |
Median |
The middle value when observations are ordered. |
14 |
Skew |
A lopsided distribution; right-skewed data have a long tail of large values that pulls the mean above the median. |
15 |
Standard deviation |
A measure of typical distance from the mean. |
16 |
Variance |
The squared version of standard deviation. |
17 |
Percentile |
A value below which a given percentage of observations fall. |
18 |
Interquartile range (IQR) |
The 75th percentile minus the 25th percentile: the width of the middle 50% of the data. |
19 |
Outlier |
An unusually large or small value, often flagged as more than 1.5 IQRs beyond the quartiles. |
20 |
Central Limit Theorem |
Sums and averages of many independent values tend toward a normal distribution, even when single values are not normal. |
21 |
Sample |
A subset of observations drawn from a larger population. |
22 |
Population |
The full group or process being studied. |
23 |
Parameter |
A numeric summary of a population. |
24 |
Statistic |
A numeric summary computed from a sample. |
25 |
Sampling variation |
The natural difference among statistics from different samples. |
26 |
Sampling distribution |
The distribution of a statistic, such as a sample mean or proportion, across many repeated samples. |
27 |
Standard error |
The standard deviation of a sampling distribution: how far a statistic typically falls from the parameter. |
28 |
Margin of error |
About 2 standard errors; roughly 95% of sample estimates fall within this distance of the parameter. |
29 |
Simulation |
Using repeated random trials to study possible outcomes. |
30 |
Descriptive statistics |
Numeric summaries that describe a dataset. |
31 |
Uncertainty |
Limited knowledge about an outcome, parameter, or decision. |