standard deviation of the sample mean
The standard deviation of the sample mean is a measure of the variability or spread of the sample means from different samples taken from the same population
The standard deviation of the sample mean is a measure of the variability or spread of the sample means from different samples taken from the same population.
To understand the concept, let’s consider a population with a known standard deviation σ. If we take multiple samples from this population, calculate the mean of each sample, and record these sample means, we can calculate the standard deviation of these sample means.
The formula to calculate the standard deviation of the sample mean is given by:
Standard Deviation of Sample Mean (σx̄) = σ / √n
In this formula, σ represents the population standard deviation, and n represents the sample size. The standard deviation of the sample mean is inversely proportional to the square root of the sample size. This means that as the sample size increases, the standard deviation of the sample mean decreases. A larger sample size leads to a more precise estimate of the population mean.
The standard deviation of the sample mean allows us to assess how much the sample means are likely to deviate from the true population mean. It helps in understanding the variability in estimates obtained from different samples.
In statistical theory, the standard deviation of the sample mean is also known as the standard error of the mean (SE). It is particularly useful in inferential statistics when trying to make inferences or draw conclusions about a population based on sample data.
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