Math Problem Statement

This data is from a sample. Calculate the mean, standard deviation, and variance. Suggestion: use technology. Round answers to two decimal places.

x 16.9 48.3 49 48.6 45.3 32.2 32.9 47

Mean =

Standard Deviation =

Variance =

Solution

The calculations for the given data are as follows:

  • Mean = 40.03
  • Standard Deviation = 11.62
  • Variance = 135.11

Would you like further explanation or have any other questions?

Here are 5 related questions to explore further:

  1. How does sample variance differ from population variance?
  2. What would be the impact of adding an outlier to this data set?
  3. How do you interpret the standard deviation in this context?
  4. How is the variance used to measure the spread of data?
  5. What are other ways to visualize the spread of this data?

Tip: Always distinguish between sample and population calculations—using n1n-1 for samples ensures an unbiased estimate.

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Math Problem Analysis

Mathematical Concepts

Descriptive Statistics
Measures of Central Tendency
Measures of Dispersion

Formulas

Mean formula: (Σx) / n
Sample Standard Deviation formula: sqrt(Σ(x - μ)² / (n - 1))
Sample Variance formula: Σ(x - μ)² / (n - 1)

Theorems

Central Limit Theorem
Law of Large Numbers

Suitable Grade Level

Grades 9-12