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The standard deviation is a measure of the spread of data about the mean. Although it is essentially a measure of the spread, the fact that it is the spread ABOUT THE MEAN that is being measured means that it does depend on the value of the mean.

However, the SD is not affected by a translation of the data. What that means is that if I add any fixed number to each data point, the mean will increase by that number, but the SD will be unchanged.

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Q: Does the value of the standard deviation depend on the value of the mean?
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Does the size of the standard deviation of a data set depend on where the center is?

Yes it does. The center, which is the mean, affects the standard deviation in a potisive way. The higher the mean is, the bigger the standard deviation.


What does it mean if the standard deviation is gr?

The answer will depend on what "gr" is.The answer will depend on what "gr" is.The answer will depend on what "gr" is.The answer will depend on what "gr" is.


What does denominator of z-score measure?

The standard deviation.z-score of a value=(that value minus the mean)/(standard deviation)


What are importance of mean and standard deviation in the use of normal distribution?

For data sets having a normal distribution, the following properties depend on the mean and the standard deviation. This is known as the Empirical rule. About 68% of all values fall within 1 standard deviation of the mean About 95% of all values fall within 2 standard deviation of the mean About 99.7% of all values fall within 3 standard deviation of the mean. So given any value and given the mean and standard deviation, one can say right away where that value is compared to 60, 95 and 99 percent of the other values. The mean of the any distribution is a measure of centrality, but in case of the normal distribution, it is equal to the mode and median of the distribtion. The standard deviation is a measure of data dispersion or variability. In the case of the normal distribution, the mean and the standard deviation are the two parameters of the distribution, therefore they completely define the distribution. See: http://en.wikipedia.org/wiki/Normal_distribution


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.

Related questions

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.


Does the size of the standard deviation of a data set depend on where the center is?

Yes it does. The center, which is the mean, affects the standard deviation in a potisive way. The higher the mean is, the bigger the standard deviation.


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.


Is the expected value the same as the standard deviation?

No. The expected value is the mean!


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.


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 does it mean if the standard deviation is gr?

The answer will depend on what "gr" is.The answer will depend on what "gr" is.The answer will depend on what "gr" is.The answer will depend on what "gr" is.


What does denominator of z-score measure?

The standard deviation.z-score of a value=(that value minus the mean)/(standard deviation)


What is the average distance of each data value from the mean?

The standard deviation.


What would it mean if a standard deviation was calculated to equal 0?

A standard deviation of zero means that all the data points are the same value.


If quartile deviation is 24. find mean deviation and standard deviation?

Information is not sufficient to find mean deviation and standard deviation.


What are importance of mean and standard deviation in the use of normal distribution?

For data sets having a normal distribution, the following properties depend on the mean and the standard deviation. This is known as the Empirical rule. About 68% of all values fall within 1 standard deviation of the mean About 95% of all values fall within 2 standard deviation of the mean About 99.7% of all values fall within 3 standard deviation of the mean. So given any value and given the mean and standard deviation, one can say right away where that value is compared to 60, 95 and 99 percent of the other values. The mean of the any distribution is a measure of centrality, but in case of the normal distribution, it is equal to the mode and median of the distribtion. The standard deviation is a measure of data dispersion or variability. In the case of the normal distribution, the mean and the standard deviation are the two parameters of the distribution, therefore they completely define the distribution. See: http://en.wikipedia.org/wiki/Normal_distribution