Standard Error of the Mean: Concept and Formula | Statistics Tutorial #6 | MarinStatsLectures
Updated: February 23, 2025
Summary
The video delves into the statistical concept of standard error of the sample mean, emphasizing that it is Sigma (population standard deviation) over square root of n. It explains how the variance of a constant times X and the sum of two independent variables influence the variance. By deriving the variance of the sample mean in relation to the variance of X and the sample size n, it elucidates the calculation leading to the formula: standard deviation of the sample mean equals Sigma over square root of n.
Introduction to Standard Deviation of Sample Mean
Explains why the standard deviation of the sample mean or standard error of the sample mean is Sigma over square root of n.
Variance of a Constant Times X
Discusses the variance of a constant times X and the variance of the sum of two independent variables.
Calculating Variance of Sample Mean
Derives the variance of the sample mean expressed in terms of the variance of X and the sample size n.
Deriving Standard Deviation of Sample Mean
Breaks down the calculation leading to the formula that the standard deviation of the sample mean is Sigma over square root of n.
FAQ
Q: What does the standard deviation of the sample mean represent?
A: The standard deviation of the sample mean represents the variability or dispersion of sample means around the population mean.
Q: How is the standard error of the sample mean related to Sigma and n?
A: The standard error of the sample mean is Sigma divided by the square root of n, where Sigma is the standard deviation of the population and n is the sample size.
Q: Can you explain the variance of a constant times X?
A: The variance of a constant times X is equal to the constant squared times the variance of X.
Q: What is the variance of the sum of two independent variables?
A: The variance of the sum of two independent variables is the sum of the variances of each individual variable.
Q: How is the variance of the sample mean derived in terms of the variance of X and sample size n?
A: The variance of the sample mean is the variance of X divided by n, where n is the sample size.
Q: What calculation leads to the formula that the standard deviation of the sample mean is Sigma over square root of n?
A: The calculation involves taking the square root of the variance of the sample mean, which results in Sigma divided by the square root of n.
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