Math Problem Statement

This data is from a sample. Calculate the mean, standard deviation, and variance. Then, calculate the population standard deviation.

Solution

Here are the calculations based on the given dataHere are the calculations based on the given

  • Sample Mean = 31.98
  • Sample Standard Deviation = 6.53
  • Sample Variance = 42.67
  • Population Standard Deviation = 6.11

Would you like a more detailed explanation or further assistance with these results?

Here are 5 related questions to expand your understanding:

  1. How does the calculation differ between a sample and a population?
  2. What is the significance of the degrees of freedom in standard deviation calculations?
  3. How does the variance relate to the standard deviation?
  4. Why is it important to know whether you're working with a sample or a population?
  5. Can you explain how outliers affect the mean and standard deviation?

Tip: For a dataset with only a few values, outliers can significantly affect both the mean and standard deviation, so it's important to analyze them separately.

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Math Problem Analysis

Mathematical Concepts

Statistics
Sample vs Population
Mean
Standard Deviation
Variance

Formulas

Sample Mean = (Σx) / n
Sample Standard Deviation = sqrt[(Σ(x - mean)^2) / (n - 1)]
Sample Variance = (Σ(x - mean)^2) / (n - 1)
Population Standard Deviation = sqrt[(Σ(x - mean)^2) / n]

Theorems

Law of Large Numbers
Central Limit Theorem

Suitable Grade Level

Grades 9-12, College Level Statistics