Explanation 1
Range uses only the endpoints.
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Lesson 4 of 15
Build variability from deviations and distinguish sample from population formulas and units.
Theory
Build variability from deviations and distinguish sample from population formulas and units. The examples in this lesson use fictional STATLAB Academy business data and independently written explanations.
Explanation 1
Range uses only the endpoints.
Explanation 2
Variance averages squared deviations.
Explanation 3
Standard deviation returns to the original measurement units.
Notation and formulas
s^2 = sum((x_i - x-bar)^2) / (n - 1)
Build variability from deviations and distinguish sample from population formulas and units.
Interactive Mission
Mean
7.00
Variance
5.00
Divide by n - 1
Standard deviation
2.24
Original units
| Value | Deviation | Squared deviation |
|---|---|---|
| 4 | -3.00 | 9.00 |
| 6 | -1.00 | 1.00 |
| 7 | 0.00 | 0.00 |
| 8 | 1.00 | 1.00 |
| 10 | 3.00 | 9.00 |
R connection
Run and edit the code, inspect printed output, and use the movable R Code Guide for line-by-line help.
Live R Lab
Build sample and population variance from deviations and compare datasets with equal means.
Ready to run
Worked example
Scenario
A fictional training organization needs to use range, variance, and standard deviation to support an operational decision.
The best summary is the one that fits the question, data structure, units, and distribution.
Interpretation safeguard
Variance is in squared units; standard deviation is in the original units.
Dataset provenance
Original synthetic data generated for STATLAB Academy. No textbook data used.
Reflection
Name the question, data structure, units, chosen method, and one limitation.
Assistant
Coach me through Range, Variance, and Standard Deviation without giving direct quiz answers or writing my final report. Ask me to justify assumptions, units, and interpretation.
Exit check
Use a hint before checking if needed. Explanations appear only after an answer is submitted.
Checkpoint
Question 1 of 2. Answered 0/2. Passing score: 70%.