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:
- How does sample variance differ from population variance?
- What would be the impact of adding an outlier to this data set?
- How do you interpret the standard deviation in this context?
- How is the variance used to measure the spread of data?
- What are other ways to visualize the spread of this data?
Tip: Always distinguish between sample and population calculations—using 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
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