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Standard deviation is the square root of the sum of the squares of the deviations of each item from the mean, i.e. the square root of the variance. In order to increase the standard deviation, therefore, you need to increase the average deviation from the mean.
There are many ways to do this. One is to move each item further away from the mean. For example, take the set [2, 4, 4, 4, 5, 5, 7, 9]. It has a mean of 5 and a standard deviation of 2.14. Multiply each item by 2.2 and subtract 5, giving the set [-1.3, 2.9, 2.9, 2.9, 5, 5, 9.2, 13.4], effectively moving each item 10% further away from the mean. This still has a mean of 5, but the standard deviation is 4.49.
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What is the relationship between the relative size of the starndard deviation and the kurtosis of a distribution?
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).
Is the mean for a set of data always greater than the standard deviation?
Yes; the standard deviation is the square root of the mean, so it will always be larger.
What does one standard deviation mean?
Standard deviation is a measure of variation from the mean of a data set. 1 standard deviation from the mean (which is usually + and - from mean) contains 68% of the data.
In research how to define standard deviation?
Standard deviation shows how much variation there is from the "average" (mean). A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
What is the relationship between standard deviation and variance for the same sample data?
The standard deviation is the square root of the variance.
