Math Problem Statement
Compute the (sample) variance and standard deviation of the data sample. (Round your answers to two decimal places.) 4.4, −4.8, 2.9, −0.4, −0.4 variance Incorrect: Your answer is incorrect. standard deviation
Solution
Let's calculate the sample variance and sample standard deviation for the data sample provided: .
Step-by-Step Solution
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Calculate the Mean:
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Calculate the Differences from the Mean and Square Them:
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Calculate the Sum of Squared Differences:
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Calculate the Sample Variance: Since this is a sample, divide by (where ):
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Calculate the Sample Standard Deviation:
Final Answers
- Variance:
- Standard Deviation:
Would you like further details on these calculations or explanations?
Here are five related questions to deepen understanding:
- What is the difference between sample variance and population variance?
- How would the calculations change if we were finding the population variance instead?
- How does rounding impact the accuracy of variance and standard deviation?
- What are practical interpretations of variance and standard deviation in a data sample?
- How does variance behave when all data points are shifted by the same constant?
Tip: Always check whether you're working with a sample or population, as this affects whether you divide by or .
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Math Problem Analysis
Mathematical Concepts
Statistics
Variance
Standard Deviation
Formulas
Sample variance formula: σ² = Σ(xᵢ - x̄)² / (n - 1)
Standard deviation formula: σ = √(variance)
Theorems
Formula for sample variance
Formula for sample standard deviation
Suitable Grade Level
Grades 9-12
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