SAMPLING DISTRIBUTION Meaning and
Definition
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A sampling distribution refers to the probability distribution that depicts the outcomes or values derived from different samples taken from a population. It provides a theoretical representation of all possible sample outcomes that could be obtained by repeatedly sampling from the same population. The concept of a sampling distribution is fundamental in statistical inference as it allows for making inferences about a population based on a sample.
In simpler terms, a sampling distribution is a collection of statistics or values derived from various samples taken from a larger population. These samples are chosen using a specific sampling method, such as simple random sampling, stratified sampling, or cluster sampling. Each sample is analyzed, and a particular statistic (e.g., mean, proportion, standard deviation) is calculated for each sample.
The sampling distribution is characterized by certain key properties, including its shape, center, and variability. For many statistics, as the sample size increases, the sampling distribution tends to become approximately normally distributed, exhibiting a bell shape. The center of the sampling distribution corresponds to the population parameter being estimated, such as the population mean or proportion. The variability of the sampling distribution is determined by the population variability and the sample size.
By studying the properties of the sampling distribution, statisticians can make inferences about the population parameters. Confidence intervals and hypothesis tests rely on the knowledge of sampling distributions to estimate and compare population parameters accurately. Therefore, understanding the concept of a sampling distribution is essential for sound statistical analysis and interpretation.
Etymology of SAMPLING DISTRIBUTION
The word "sampling" comes from the Old English word "sampol" meaning "example" or "pattern". It evolved from the Latin word "exemplum" meaning "example" as well. "Distribution" comes from the Latin word "distributio" meaning "division" or "distribution". Therefore, the etymology of the term "sampling distribution" can be traced back to the combination of these two words, indicating the division or distribution of examples or patterns obtained through sampling.
