Explanation 1
Deviation: A support value minus the mean.
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Lesson 5 of 18
Measure probability-weighted dispersion and interpret standard deviation in the original units.
Core lesson
Measure probability-weighted dispersion and interpret standard deviation in the original units.
Explanation 1
Deviation: A support value minus the mean.
Explanation 2
Variance: Expected squared deviation.
Explanation 3
Standard deviation: Nonnegative square root of variance.
Terminology
A support value minus the mean.
Demand above expected demand.
Expected squared deviation.
Squared service units.
Nonnegative square root of variance.
Service units.
Notation and formulas
Var(X)=sum_x (x-mu)^2p(x); SD(X)=sqrt(Var(X))
Define X, its support, parameters, units, and assumptions before substituting values.
Interactive Mission
Inspect probability-weighted squared deviations from the mean.
P(X = x)
0.2
F(x) = P(X <= x)
0.9
E(X)
3
SD(X)
1.0954
| x | P(X=x) | Included in F(4) |
|---|---|---|
| 1 | 0.1 | Yes |
| 2 | 0.2 | Yes |
| 3 | 0.4 | Yes |
| 4 | 0.2 | Yes |
| 5 | 0.1 | No |
Interpretation: Custom PMF, discrete uniform, Bernoulli, or binomial: inspect support and trial structure before choosing.
Worked example
Scenario
Two plans have the same expected demand but different concentration.
Center alone cannot describe operational risk.
R connection
Run and edit the original script, inspect intermediate output, and keep exact and approximate results clearly labelled.
Live R Lab
Calculate center, risk, and expected profit from a custom demand PMF.
Ready to run
Dataset provenance
Original synthetic data generated for STATLAB Academy. No textbook data used.
Interpretation safeguard
Do not compare variance directly across variables with different units; use an appropriate scale and context.
Reflection
Name the random variable, support, parameters, units, dependence assumptions, and one limitation.
Assistant
Coach me through Variance, Standard Deviation, and Discrete Risk by asking about X, support, parameters, assumptions, probability notation, exact versus approximate status, and interpretation. Do not provide a quiz answer before submission or write my final capstone recommendation.
Exit check
Use conceptual hints before submitting. Full formulas, calculations, and interpretation appear afterward.
Checkpoint
Question 1 of 2. Answered 0/2. Passing score: 70%.
Resource
Explore additional discrete-distribution explanations from properly licensed or publisher resources.
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