Final answer:
Sample means have less standard deviation than population standard deviation because the standard deviation of a sample mean is divided by the square root of the sample size, making it a more precise estimate of the population mean.
Step-by-step explanation:
When calculating the standard deviation of a sample mean, it is divided by the square root of the sample size, while the standard deviation of a population is calculated using the entire population. This leads to the sample mean having a smaller standard deviation compared to the population standard deviation.
For example, let's consider a population with a mean of 100 and a standard deviation of 20. If we take a sample of size 10, the standard deviation of the sample mean would be 20 / √10, which is approximately 6.32. This is smaller than the population standard deviation of 20.
The smaller standard deviation of the sample mean indicates that the sample mean is a more precise estimate of the population mean, as it is less affected by individual data points.