Study Notes: Introduction to Sampling Distributions and Variability

Parameter

A number that describes a characteristic of a population.

Statistic

A number that describes a characteristic of a sample.

Sample Size (n)

The number of observations in a sample.

Sampling Distribution

The probability distribution of a statistic for all possible samples of the same size from a population.

Population Distribution

The distribution of values of a variable among all individuals in the population.

Distribution of Sample Data

The distribution of values within a single sample.

Sampling Variability

The fact that different random samples produce different values for a statistic.

Unbiased Estimator

A statistic is an unbiased estimator if the mean of its sampling distribution equals the true population parameter.

Point Estimator

A statistic that provides an estimate of a population parameter.

Biased Estimator

A statistic is biased if the mean of its sampling distribution consistently overestimates or underestimates the parameter.

Mean of Sampling Distribution

The average of all sample means from repeated sampling.

High Bias

When sample estimates are clustered but far from the true parameter.

High Variability

When sample estimates are spread out widely around the true parameter.

Low Bias, Low Variability

When all sample estimates are tightly clustered around the true parameter.

10% Condition

A guideline stating the population must be at least 10 times larger than the sample size.

$ar{x}$ (x-bar)

The sample mean, a statistic that estimates the population mean.

$
ho$ (rho)

A symbol commonly used to represent a proportion in statistics.

$ heta$ (theta)

A common parameter symbol, used to represent various population characteristics.

$p$ (lowercase p)

The true population proportion.

$ ext{prop.}$ (hat p)

The sample proportion, an estimate of the population proportion.

Standard Deviation of Sampling Distribution

The spread of the sampling distribution, affected by sample size.

Notation Guide

A reference for correct statistical symbols for population parameters and sample statistics.

Statistical Outliers

Values that significantly differ from other observations, impacting averages.

Theoretical Graph

A graph representing statistics from many samples rather than raw data from one sample.

Precision in Estimation

The closeness of sample statistics to the actual population parameter.

Random Sampling

The process of selecting a sample in such a way that each member of the population has an equal chance of being included.