AP Stats

Parameter

A numerical value that describes a specific characteristic of an entire population.

Population

The entire group of individuals or instances about whom we hope to learn.

Population Mean

Denoted by the Greek letter μ, it represents the average of all values in a population.

Population Proportion

Denoted by p, it represents the proportion of a certain characteristic in the population.

Population Standard Deviation

Denoted by the Greek letter σ, it measures the dispersion of a population's values.

Statistic

A numerical value that describes a characteristic of a sample.

Sample Mean

Denoted by x̄ (x-bar), used to estimate the population mean μ.

Sample Proportion

Denoted by ŷ (p-hat), used to estimate the population proportion p.

Sample Standard Deviation

Denoted by s, it estimates the population standard deviation σ.

Sampling Variability

The natural phenomenon that a statistic will vary from sample to sample.

Low Bias

When the average of the sampling distribution equals the true population parameter.

Low Variability

The spread of the sampling distribution is small, leading to more consistent estimates.

Unbiased Estimator

A statistic that does not systematically over- or under-estimate a population parameter.

High Bias, Low Variability

Estimates are consistently wrong but tightly clustered together.

Low Bias, High Variability

Estimates are centered but widely scattered around the true value.

Central Limit Theorem (CLT)

The theory that states the sampling distribution of the sample mean will be approximately normal if the sample size is sufficiently large.

Large Sample Condition

The rule that the CLT applies if the sample size n is 30 or more.

10% Condition

A guideline ensuring that the sample size n is no more than 10% of the population size N to treat observations as independent.

Independent Observations

A situation where the selection of one individual does not affect the selection of another.

Standard Deviation Formula for Means

The formula σ_x̄ = σ/n for calculating the standard deviation of the sampling distribution of the sample mean.

Standard Deviation Formula for Proportions

The formula σ_ŷ = √(p(1-p)/n) for calculating the standard deviation of the sampling distribution of the sample proportion.

Point Estimator

A statistic that provides a single best estimate of a population parameter.

Clustered Estimates

Estimates that are close to each other in value but may be far from the true population parameter.

Population Distribution

The distribution of a characteristic (e.g., height, weight) across the entire population.

Estimate Accuracy

A measure of how close the estimates are to the actual population parameters.

Sample Size n

The number of observations or individuals included in a sample.

Population Size N

The total number of individuals or instances in the population.