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The sample standard deviation (s) divided by the square root of the number of observations in the sample (n).
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.
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.
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.
A small sample and a large 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.
The sample standard deviation (s) divided by the square root of the number of observations in the sample (n).
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.
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.
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.
A small sample and a large 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.
The mean is the average value and the standard deviation is the variation from the mean value.
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.
No. To calculate a sample standard deviation one requires the sample values. The five-number summary provides only the lowest value, the highest, the median, and the upper and lower quartiles. In any sample of size greater than five some values will be missing from the summary.
No. The standard deviation is not exactly a value but rather how far a score deviates from the mean.
The standard error of the mean and sampling error are two similar but still very different things. In order to find some statistical information about a group that is extremely large, you are often only able to look into a small group called a sample. In order to gain some insight into the reliability of your sample, you have to look at its standard deviation. Standard deviation in general tells you spread out or variable your data is. If you have a low standard deviation, that means your data is very close together with little variability. The standard deviation of the mean is calculated by dividing the standard deviation of the sample by the square root of the number of things in the sample. What this essentially tells you is how certain are that your sample accurately describes the entire group. A low standard error of the mean implies a very high accuracy. While the standard error of the mean just gives a sense for how far you are away from a true value, the sampling error gives you the exact value of the error by subtracting the value calculated for the sample from the value for the entire group. However, since it is often hard to find a value for an entire large group, this exact calculation is often impossible, while the standard error of the mean can always be found.