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Sampling Distribution of the Sample Mean and Central Limit Theorem definitions

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  • Population Mean
    The average value for an entire group, often unknown and estimated using sample data.
  • Sample Mean
    The average value calculated from a subset of the population, used to estimate the population average.
  • Random Sample
    A subset of individuals chosen from a population where each member has an equal chance of selection.
  • Sampling Error
    The difference between a sample statistic and the actual population parameter due to random chance.
  • Sampling Distribution
    The probability distribution of a statistic, such as the sample mean, from repeated samples of the same size.
  • Central Limit Theorem
    A principle stating that the sampling distribution of the sample mean approaches normality as sample size increases.
  • Normal Distribution
    A symmetric, bell-shaped curve describing the spread of a variable where most values cluster around the mean.
  • Z-Score
    A standardized value indicating how many standard deviations a statistic is from the mean of its distribution.
  • Population Standard Deviation
    A measure of variability for an entire group, reflecting how much individual values differ from the mean.
  • Sample Size
    The number of observations or data points included in a single sample from the population.
  • Histogram
    A graphical representation showing the frequency distribution of a set of data, often used for visualizing distributions.
  • Right Skew
    A distribution shape where most values are concentrated on the left, with a long tail extending to the right.
  • Probability
    A numerical measure of the likelihood that a specific event or outcome will occur.
  • Statistic
    A numerical value calculated from sample data, used to estimate a population parameter.
  • Parameter
    A numerical value summarizing a characteristic of an entire population, such as its mean or standard deviation.