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What is the value of the standard error of the sample mean?
The sample standard deviation (s) divided by the square root of the number of observations in the sample (n).
Is sample standard deviation the same as standard deviation?
No, the standard deviation is a measure of the entire population. The sample standard deviation is an unbiased estimator of the population. It is different in notation and is written as 's' as opposed to the greek letter sigma. Mathematically the difference is a factor of n/(n-1) in the variance of the sample. As you can see the value is greater than 1 so it will increase the value you get for your sample mean. Essentially, this covers for the fact that you are unlikely to obtain the full population variation when you sample.
What does relative standard deviation of 0.003 mean?
The relative standard deviation is the absolute value of the ration of the sample mean to the sample standard deviation. This value appears to be quite small; however, without comparative data it is difficult to know what to make of it. In some contexts it might even be considered large.
Why is the standard error a smaller numerical value compared to the standard deviation?
Let sigma = standard deviation. Standard error (of the sample mean) = sigma / square root of (n), where n is the sample size. Since you are dividing the standard deviation by a positive number greater than 1, the standard error is always smaller than the standard deviation.
What combination of factors will produce the smallest value for the standard error?
A small sample and a large standard deviation
Sample standard deviation?
Standard deviation in statistics refers to how much deviation there is from the average or mean value. Sample deviation refers to the data that was collected from a smaller pool than the population.
What is the value of the standard error of the sample mean?
The sample standard deviation (s) divided by the square root of the number of observations in the sample (n).
Is sample standard deviation the same as standard deviation?
No, the standard deviation is a measure of the entire population. The sample standard deviation is an unbiased estimator of the population. It is different in notation and is written as 's' as opposed to the greek letter sigma. Mathematically the difference is a factor of n/(n-1) in the variance of the sample. As you can see the value is greater than 1 so it will increase the value you get for your sample mean. Essentially, this covers for the fact that you are unlikely to obtain the full population variation when you sample.
What does relative standard deviation of 0.003 mean?
The relative standard deviation is the absolute value of the ration of the sample mean to the sample standard deviation. This value appears to be quite small; however, without comparative data it is difficult to know what to make of it. In some contexts it might even be considered large.
Why is the standard error a smaller numerical value compared to the standard deviation?
Let sigma = standard deviation. Standard error (of the sample mean) = sigma / square root of (n), where n is the sample size. Since you are dividing the standard deviation by a positive number greater than 1, the standard error is always smaller than the standard deviation.
What combination of factors will produce the smallest value for the standard error?
A small sample and a large standard deviation
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 difference between standard deviation and mean?
The mean is the average value and the standard deviation is the variation from the mean value.
How standard deviation and Mean deviation differ from each other?
There is 1) standard deviation, 2) mean deviation and 3) mean absolute deviation. The standard deviation is calculated most of the time. If our objective is to estimate the variance of the overall population from a representative random sample, then it has been shown theoretically that the standard deviation is the best estimate (most efficient). The mean deviation is calculated by first calculating the mean of the data and then calculating the deviation (value - mean) for each value. If we then sum these deviations, we calculate the mean deviation which will always be zero. So this statistic has little value. The individual deviations may however be of interest. See related link. To obtain the means absolute deviation (MAD), we sum the absolute value of the individual deviations. We will obtain a value that is similar to the standard deviation, a measure of dispersal of the data values. The MAD may be transformed to a standard deviation, if the distribution is known. The MAD has been shown to be less efficient in estimating the standard deviation, but a more robust estimator (not as influenced by erroneous data) as the standard deviation. See related link. Most of the time we use the standard deviation to provide the best estimate of the variance of the population.
Can The standard deviation of a distribution be a negative value?
No. The standard deviation is not exactly a value but rather how far a score deviates from the mean.
If your mean is 33.7 and your standard deviation is 33.7 what is your z score?
Z-score is the x value minus the mean, all divided by the standard deviation; or z=(x-mu)/sigma. The "x" value needs to be given to answer the question.
Why does the formula for standard deviation have a square root in it?
The formula for standard deviation has both a square (which is a power of 2) and a square-root (a power of 1/2). Both must be there to balance each other, to keep the standard deviation value's magnitude similar to (having the same units as) the sample numbers from which it's calculated. If either is removed from the formula, the resulting standard deviation value will have different units, reducing its usefulness as a meaningful statistic.
