The answer depends on the underlying variance (standard deviation) in the population, the size of the sample and the procedure used to select the sample.
The sample standard error.
Random error.
The sample mean will seldom be the same as the population mean due to sampling error. See the related link.
Standard error of the sample mean is calculated dividing the the sample estimate of population standard deviation ("sample standard deviation") by the square root of sample size.
Zero
Sampling Error
standard error
0. The expected value of the sample mean is the population mean, so the expected value of the difference is 0.
No.
The sample standard error.
Random error.
The sample mean will seldom be the same as the population mean due to sampling error. See the related link.
Standard error of the sample mean is calculated dividing the the sample estimate of population standard deviation ("sample standard deviation") by the square root of sample size.
Standard error (SE) measures the accuracy with which a sample statistic estimates a population parameter. It quantifies the variability of the sample mean from the true population mean, indicating how much the sample mean is expected to fluctuate due to random sampling. A smaller standard error suggests more precise estimates, while a larger standard error indicates greater variability and less reliability in the sample mean. Essentially, SE helps in understanding the precision of sample estimates in relation to the overall population.
The sampling error is the error one gets from observing a sample instead of the whole population. The bigger it is, the less faith you should have that your sample represents the true value in the population. If it is zero, your sample is VERY representative of the population and you can trust that your result is true of the population.
A low standard error indicates that the sample mean is a precise estimate of the population mean, suggesting that the sample data is closely clustered around the sample mean. It implies that there is less variability in the sample means across different samples, leading to more reliable statistical inferences. In essence, a low standard error reflects high confidence in the accuracy of the sample mean as a representation of the population.
The sample standard deviation is used to derive the standard error of the mean because it provides an estimate of the variability of the sample data. This variability is crucial for understanding how much the sample mean might differ from the true population mean. By dividing the sample standard deviation by the square root of the sample size, we obtain the standard error, which reflects the precision of the sample mean as an estimate of the population mean. This approach is particularly important when the population standard deviation is unknown.