Math Problem Statement

The following data represent the amount of time (in minutes) a random sample of eight students took to complete the online portion of an exam. Compute the range, sample variance, and sample standard deviation time. Data: 60, 128, 85, 122, 79, 95, 85, 90.

Solution

Here are the computed values based on the provided dataHere are the computed values based on the provided

  • Range: 68 minutes
  • Sample Standard Deviation: 22.34 minutes (rounded to two decimal places)
  • Sample Variance: 498.86 minutes² (rounded to two decimal places)

Would you like more details on any of these calculations? Here are five related questions you might explore:

  1. How is the range calculated, and what does it signify in data analysis?
  2. What is the difference between sample variance and population variance?
  3. How does the standard deviation help in understanding data dispersion?
  4. Why is the degree of freedom (ddof=1) used when calculating sample variance?
  5. How do these statistical measures relate to normal distribution?

Tip: Always remember to round to an appropriate number of decimal places based on the context of the problem!

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Math Problem Analysis

Mathematical Concepts

Descriptive Statistics
Variance
Standard Deviation
Range

Formulas

Range = Max value - Min value
Sample variance (s²) = Σ(xi - x̄)² / (n - 1)
Sample standard deviation (s) = sqrt(variance)

Theorems

Descriptive Statistics Measures
Empirical Rule (in relation to standard deviation)

Suitable Grade Level

Grades 10-12

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