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The 'standard deviation' in statistics or probability is a measure of how spread out the numbers are. It mathematical terms, it is the square root of the mean of the squared deviations of all the numbers in the data set from the mean of that set.
It is approximately equal to the average deviation from the mean.
If you have a set of values with low standard deviation, it means that in general, most of the values are close to the mean. A high standard deviation means that the values in general, differ a lot from the mean.
The variance is the standard deviation squared. That is to say, the standard deviation is the square root of the variance. To calculate the variance, we simply take each number in the set and subtract it from the mean. Next square that value and do the same for each number in the set. Lastly, take the mean of all the squares. The mean of the squared deviation from the mean is the variance. The square root of the variance is the standard deviation.
If you take the following data series for example, the mean for all of them is '3'.
3, 3, 3, 3, 3, 3 all the values are 3, they're the same as the mean. The standard deviation is zero. This is because the difference from the mean is zero in each case, and after squaring and then taking the mean, the variance is zero. Last, the square root of zero is zero so the standard deviation is zero. Of note is that since you are squaring the deviations from the mean, the variance and hence the standard deviation can never be negative.
1, 3, 3, 3, 3, 5 - most of the values are the same as the mean. This has a low standard deviation. In this case, the standard deviation is very small since most of the difference from the mean are small.
1, 1, 1, 5, 5, 5 - all the values are two higher or two lower than the mean. This series has the highest standard deviation.
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What is the relationship between standard deviation and variance for the same sample data?
The standard deviation is the square root of the variance.
What is the relationship between standard deviation and precision?
The more precise a result, the smaller will be the standard deviation of the data the result is based upon.
What is the difference between standard deviation and margin of error?
Standard of deviation and margin of error are related in that they are both used in statistics. Level of confidence is usually shown as the Greek letter alpha when people conducting surveys allow for a margin of error - usually set at between 90% and 99%. The Greek letter sigma is used to represent standard deviation.
What is the relationship between standard deviation and accuracy?
It depends what you're asking. The question is extremely unclear. Accuracy of what exactly? Even in the realm of statistics an entire book could be written to address such an ambiguous question (to answer a myriad of possible questions). If you simply are asking what the relationship between the probability that something will occur given the know distribution of outcomes (such as a normal distribution), the mean of that that distribution, and the the standard deviation, then the standard deviation as a represents the spread of the curve of probability. This means that if you had a cure where 0 was the mean, and 3 was the standard deviation, the likelihood of observing a value of 12 (or -12) would be likely inaccurate if that was your prediction. However, if you had a mean of 0 and a standard deviation of 100, the likelihood of observing of a 12 (or -12) would be quite likely. This is simply because the standard deviation provides a simple representation of the horizontal spread of probability on the x-axis.
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.
