Math Problem Statement
Solution
The question asks which of the following is a biased estimator, meaning which does not accurately target the population parameter.
Here's an analysis of the options:
- Median - The sample median is typically an unbiased estimator of the population median.
- Proportion - The sample proportion is an unbiased estimator of the population proportion.
- Variance - The sample variance (calculated as ) is an unbiased estimator of the population variance. However, if calculated using , it becomes biased.
- Mean - The sample mean is an unbiased estimator of the population mean.
Answer: The correct answer is Variance, when it is calculated using , as this does not accurately target the population variance and is considered a biased estimator.
Would you like more details or have any further questions? Here are some related questions you could explore:
- Why does dividing by rather than give an unbiased variance estimate?
- What are other common examples of biased and unbiased estimators?
- How do you calculate the sample mean and population mean?
- What is the significance of biased vs. unbiased estimators in statistical inference?
- How does sample size affect the accuracy of different estimators?
Tip: Remember, an unbiased estimator has an expected value equal to the parameter it estimates.
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Math Problem Analysis
Mathematical Concepts
Statistics
Estimators
Population Parameters
Formulas
Variance formula: 1/n or 1/(n-1) ∑(x_i - x̄)^2
Theorems
Biased vs. Unbiased Estimator Theorem
Suitable Grade Level
Grades 11-12 and Undergraduate
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