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✍️ Free Response Questions (FRQs)
👆 Unit 1 - Exploring One-Variable Data
✌️ Unit 2 - Exploring Two-Variable Data
🔎 Unit 3 - Collecting Data
🎲 Unit 4 - Probability, Random Variables, and Probability Distributions
📊 Unit 5 - Sampling Distributions
⚖️ Unit 6 - Inference for Categorical Data: Proportions
😼 Unit 7 - Inference for Qualitative Data: Means
✳️ Unit 8 Inference for Categorical Data: Chi-Square
📈 Unit 9 - Inference for Quantitative Data: Slopes
🧐 Multiple Choice Questions (MCQs)
✏️ Blogs
Best Quizlet Decks for AP Statistics
- Unit 1 Key Terms (15-23%): Exploring One-Variable Data
- Unit 2 Key Terms (5-7%): Exploring Two-Variable Data
- Unit 3 Key Terms (12-15%): Collecting Data
- Unit 4 Key Terms (10-20%): Probability, Random Variables, and Probability Distributions
- Unit 5 Key Terms (7-12%): Sampling Distributions
- Unit 6 Key Terms (12-15%): Inference for Categorical Data: Proportions
- Unit 7 Key Terms (10-18%): Inference for Quantitative Data: Means
- Unit 8 Key Terms (2-5%): Inference for Categorical Data: Chi-Squared
- Unit 9 Key Terms (2-5%): Inference for Quantitative Data: Slopes
- Closing Thoughts
5.4 Biased and Unbiased Point Estimates
#exploringdata
#sampling
#experimentation
#anticipatingpatterns
#statisticalinference
⏱️ 2 min read
written by
josh argo
brianna bukowski
harrison burnside
(editor)
June 4, 2020
How to Tell if a Sample is Unbiased
A sample is unbiased if the estimator value (sample statistic) is equal to the population parameter. For example, if the sampling distribution mean (x̅) is equal to the population mean (𝝁) or if the average of our sample proportions (p)is equal to our population proportion (𝝆)..
How to Tell if a Sample has Minimum Variability
A sampling distribution has a minimum amount of variability (spread) if all samples have statistics that are approximately equivalent to one another. It is impossible to have no variability, due to the nature of random sampling. However, a larger sample size will minimize variability in a sampling distribution.
Bias and Variability
Bias is how skewed (also how screwed) the distribution is. Specifically, if an entire distribution is on the left side of our population parameter, it is skewed to the left. If a sample is equally spread out around the mean, then there is no bias.
The more spread out a distribution is, the more variability it has. The standard deviation of the sampling distribution is the estimator of the population standard deviation. If the standard deviation of the sampling distribution is equal to population standard deviation, it is said that the standard deviation of sampling distribution is the consistent estimator. High variability can be fixed by increasing your sample size, but if your sample does have high bias, there is no statistical way to fix it.
A good illustration for bias and variability is a bullseye. Bias measures how precise the archer is (how close to the bullseye), while variability measures how consistent he/she is. See the illustrations below for different circumstances regarding bias and variability:
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