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Sampling Distribution of the Sample Mean and Central Limit Theorem definitions

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  • Population Mean
    Represents the average value for all members in a population, often denoted as mu, and is the target for statistical estimation.
  • Sample Mean
    Calculated by averaging values from a random sample; used to approximate the population mean but can vary between samples.
  • Random Sample
    A subset of a population selected so each member has an equal chance of inclusion, ensuring unbiased representation.
  • Sampling Distribution
    A frequency distribution formed by collecting multiple sample means from samples of the same size, revealing their variability.
  • Central Limit Theorem
    States that as sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of population shape.
  • Normal Distribution
    A symmetric, bell-shaped curve where most values cluster around the mean, allowing for probability calculations using z-scores.
  • Sample Size
    The number of observations in each sample; larger sizes yield more reliable estimates and a more normal sampling distribution.
  • Z Score
    A standardized value indicating how many standard deviations a statistic is from the mean, used for probability calculations.
  • Probability
    A measure of how likely an event or outcome is, often calculated using the normal distribution and z-scores in sampling contexts.
  • Standard Deviation
    Quantifies the spread of values in a dataset; in sampling distributions, it decreases as sample size increases.
  • Histogram
    A graphical representation of a distribution, showing the frequency of sample means within intervals.
  • Bell Curve
    A visual shape of the normal distribution, characterized by a peak at the mean and symmetric tails.
  • Population Standard Deviation
    Measures variability among all members of a population, denoted as sigma, and used in sampling calculations.
  • Sampling Distribution Mean
    The average of all sample means in a sampling distribution, which equals the population mean under the central limit theorem.
  • Z Table
    A reference chart listing probabilities associated with z scores, used to interpret results from normal distributions.