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The standard deviation is the square root of the variance.

Q: What is the relationship between standard deviation and variance for the same sample data?

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The more precise a result, the smaller will be the standard deviation of the data the result is based upon.

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.

The answer depends on the underlying variance (standard deviation) in the population, the size of the sample and the procedure used to select the sample.

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.

It is inversely proportional; a larger standard deviation produces a small kurtosis (smaller peak, more spread out data) and a smaller standard deviation produces a larger kurtosis (larger peak, data more centrally located).

Related questions

Standard deviation is the square root of the variance.

Standard deviation is the variance from the mean of the data.

The SD is the (positive) square root of the variance.

Formally, the standard deviation is the square root of the variance. The variance is the mean of the squares of the difference between each observation and their mean value. An easier to remember form for variance is: the mean of the squares minus the square of the mean.

The variance and the standard deviation will decrease.

The mean deviation for any distribution is always 0 and so conveys no information whatsoever. The standard deviation is the square root of the variance. The variance of a set of values is the sum of the probability of each value multiplied by the square of its difference from the mean for the set. A simpler way to calculate the variance is Expected value of squares - Square of Expected value.

The more precise a result, the smaller will be the standard deviation of the data the result is based upon.

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.

There is absolutely no relationship to what you've asked. I'm pretty sure you simply framed the question in the wrong way, but to literally answer your question... none. Zero relationship. There's no such thing. There is however a relationship between standard deviation and a CI, but a CI can in no shape way or form influence a standard deviation.

The mean deviation (also called the mean absolute deviation) is the mean of the absolute deviations of a set of data about the data's mean. The standard deviation sigma of a probability distribution is defined as the square root of the variance sigma^2,

You can calculate standard deviation by addin the numbers of data that are together and dividing that number by the amount pieces of data.THAT IS TOTALLY INCORRECT.What was answered above was the calculation for getting an (mean) average.If you take five numbers for example 1, 2, 3, 4, 5 then the (mean) average is 3.But the standard deviation between them is 1.58814 and the variance is 2.5Also the population std. deviation will be 1.41421 and the population variance will be 2.see standard-deviation.appspot.com/

Standard deviation doesn't have to be between 0 and 1.