✍️ Free Response Questions (FRQs)
👆 Unit 1 - Exploring One-Variable Data
1.4Representing a Categorical Variable with Graphs
1.5Representing a Quantitative Variable with Graphs
1.6Describing the Distribution of a Quantitative Variable
1.7Summary Statistics for a Quantitative Variable
1.8Graphical Representations of Summary Statistics
1.9Comparing Distributions of a Quantitative Variable
✌️ Unit 2 - Exploring Two-Variable Data
2.0 Unit 2 Overview: Exploring Two-Variable Data
2.1Introducing Statistics: Are Variables Related?
2.2Representing Two Categorical Variables
2.3Statistics for Two Categorical Variables
2.4Representing the Relationship Between Two Quantitative Variables
2.8Least Squares Regression
🔎 Unit 3 - Collecting Data
3.5Introduction to Experimental Design
🎲 Unit 4 - Probability, Random Variables, and Probability Distributions
4.1Introducing Statistics: Random and Non-Random Patterns?
4.7Introduction to Random Variables and Probability Distributions
4.8Mean and Standard Deviation of Random Variables
4.9Combining Random Variables
4.11Parameters for a Binomial Distribution
📊 Unit 5 - Sampling Distributions
5.0Unit 5 Overview: Sampling Distributions
5.1Introducing Statistics: Why Is My Sample Not Like Yours?
5.4Biased and Unbiased Point Estimates
5.6Sampling Distributions for Differences in Sample Proportions
⚖️ Unit 6 - Inference for Categorical Data: Proportions
6.0Unit 6 Overview: Inference for Categorical Data: Proportions
6.1Introducing Statistics: Why Be Normal?
6.2Constructing a Confidence Interval for a Population Proportion
6.3Justifying a Claim Based on a Confidence Interval for a Population Proportion
6.4Setting Up a Test for a Population Proportion
6.6Concluding a Test for a Population Proportion
6.7Potential Errors When Performing Tests
6.8Confidence Intervals for the Difference of Two Proportions
6.9Justifying a Claim Based on a Confidence Interval for a Difference of Population Proportions
6.10Setting Up a Test for the Difference of Two Population Proportions
😼 Unit 7 - Inference for Qualitative Data: Means
7.1Introducing Statistics: Should I Worry About Error?
7.2Constructing a Confidence Interval for a Population Mean
7.3Justifying a Claim About a Population Mean Based on a Confidence Interval
7.4Setting Up a Test for a Population Mean
7.5Carrying Out a Test for a Population Mean
7.6Confidence Intervals for the Difference of Two Means
7.7Justifying a Claim About the Difference of Two Means Based on a Confidence Interval
7.8Setting Up a Test for the Difference of Two Population Means
7.9Carrying Out a Test for the Difference of Two Population Means
✳️ Unit 8 Inference for Categorical Data: Chi-Square
📈 Unit 9 - Inference for Quantitative Data: Slopes
🧐 Multiple Choice Questions (MCQs)
Is AP Statistics Hard? Is AP Statistics Worth Taking?
Best Quizlet Decks for AP Statistics
⏱️ 2 min read
June 4, 2020
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)..
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 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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