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The standard deviation of the sample means is called the standard error of the mean (SEM). It quantifies the variability of sample means around the population mean and is calculated by dividing the population standard deviation by the square root of the sample size. The SEM decreases as the sample size increases, reflecting improved estimates of the population mean with larger samples.
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What does the s stand for in statistics?
Usually s means standard deviation of a sample.
What does it means if the standard deviation is large?
that you have a large variance in the population and/or your sample size is too small
What does Sx mean in mathematics?
Sx means the sample standard deviation of the variable "x".
How do you calculate standard deviation without a normal distribution?
You calculate standard deviation the same way as always. You find the mean, and then you sum the squares of the deviations of the samples from the means, divide by N-1, and then take the square root. This has nothing to do with whether you have a normal distribution or not. This is how you calculate sample standard deviation, where the mean is determined along with the standard deviation, and the N-1 factor represents the loss of a degree of freedom in doing so. If you knew the mean a priori, you could calculate standard deviation of the sample, and only use N, instead of N-1.
Why is the standard deviation of a distribution of means smaller than the standard deviation of the population from which it was derived?
The reason the standard deviation of a distribution of means is smaller than the standard deviation of the population from which it was derived is actually quite logical. Keep in mind that standard deviation is the square root of variance. Variance is quite simply an expression of the variation among values in the population. Each of the means within the distribution of means is comprised of a sample of values taken randomly from the population. While it is possible for a random sample of multiple values to have come from one extreme or the other of the population distribution, it is unlikely. Generally, each sample will consist of some values on the lower end of the distribution, some from the higher end, and most from near the middle. In most cases, the values (both extremes and middle values) within each sample will balance out and average out to somewhere toward the middle of the population distribution. So the mean of each sample is likely to be close to the mean of the population and unlikely to be extreme in either direction. Because the majority of the means in a distribution of means will fall closer to the population mean than many of the individual values in the population, there is less variation among the distribution of means than among individual values in the population from which it was derived. Because there is less variation, the variance is lower, and thus, the square root of the variance - the standard deviation of the distribution of means - is less than the standard deviation of the population from which it was derived.
Does the distribution of sample means have a standard deviation that increases with the sample size?
No, it is not.
When the population standard deviation is not known the sampling distribution is a?
If the samples are drawn frm a normal population, when the population standard deviation is unknown and estimated by the sample standard deviation, the sampling distribution of the sample means follow a t-distribution.
What does the s stand for in statistics?
Usually s means standard deviation of a sample.
What is the difference between standard error of mean and standard deviation of means?
Standard error of the mean (SEM) and standard deviation of the mean is the same thing. However, standard deviation is not the same as the SEM. To obtain SEM from the standard deviation, divide the standard deviation by the square root of the sample size.
What does it mean for a sample to have a standard deviation of zero?
It means that there are is no variation from the mean. In other words, all values in your sample are identical.
What name do you give to the standard deviation of the sampling distribution of sample means?
the central limit theorem
What does it means if the standard deviation is large?
that you have a large variance in the population and/or your sample size is too small
What does Sx mean in mathematics?
Sx means the sample standard deviation of the variable "x".
What does it mean when the standard error value is smaller than the standard deviation?
It simply means that you have a sample with a smaller variation than the population itself. In the case of random sample, it is possible.
What is the distribution with an means of 0 and a standard deviation of 1?
It is called a standard normal distribution.
True or false a distribution of sample means is normally distributed with a mean equal to the population mean and standard deviation equal to the standard error of the mean?
True.
The standard deviation of the distribution of means is also known as the population standard deviation?
Yes.
