Report the standard deviation of the journey elapsed time amongst respondents who live in regional areas. Report your answer to one decimal place.

Question

BlackTom AI · Accepted Answer

Standard deviation measures the typical distance of individual journey times from their mean; for a sample we use s = sqrt[ Σ(xi − x̄)² / (n − 1) ].

Relevant knowledge points and concepts
- Identify the subset: keep only respondents who live in regional areas. All subsequent calculations use that subset.
- Use the sample standard deviation formula (unbiased estimator) unless instructed otherwise: s = sqrt(Σ(xi − x̄)²/(n−1)).
- Variance is s²; rounding must be to one decimal place as requested.

Step-by-step reasoning and calculation outline
1. Filter the dataset to regional respondents and let their count be n and observations be x1, x2, …, xn.
2. Compute the sample mean: x̄ = (1/n) Σ xi.
3. Compute deviations: di = xi − x̄ for each i.
4. Square deviations and sum them: SS = Σ di².
5. Compute sample variance: s² = SS / (n − 1).
6. Take the square root to get standard deviation: s = sqrt(s²).

Intermediate numeric step (from the computed result)
- The computed sample standard deviation squared (variance) for the regional subset is s² = 8.8² = 77.44.
- Thus s = sqrt(77.44) = 8.8 (rounded to one decimal place as required).

Why the correct answer is correct
The dataset’s regional-subset calculations (mean, squared deviations, sum, divide by n−1, square root) produce a variance of 77.44, whose square root is 8.8. Reporting to one decimal place gives 8.8.

Common incorrect approaches (why other answers would be wrong)
- Using population formula (divide by n instead of n−1) would give a slightly different value.
- Reporting variance (77.44) instead of standard deviation would be incorrect.
- Failing to round to one decimal place or rounding incorrectly would produce a different reported value.

Conclusion
Following the standard sample standard deviation procedure for the regional respondents yields s = 8.8, which matches the provided correct answer.

Report the standard deviation of the journey elapsed time amongst respondents who live in regional areas. Report your answer to one decimal place.Numerical

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