# 2.7 Terms

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Standard Deviation
A number that measures how far data values are from their mean. Provides a numerical measure of the overall amount of variation in a data set, and Can be used to determine whether a particular data value is close to or far from the mean.
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The standard deviation is _____ when the data are all concentrated close to the mean, exhibiting little variation or spread.
Small.
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The standard deviation is ______ when the data values are more spread out from the mean, exhibiting more variation.
Larger.
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value = mean + (#ofSTDEV)(standard deviation)
(#STDEV) does not need to be an integer.
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sample: x = x¯ + (#ofSTDEV)(s) Population: x=?+(#ofSTDEV)(?)
The lower case letter s represents the sample standard deviation and the Greek letter ? (sigma, lower case) represents the population standard deviation. The symbol x¯ is the sample mean and the Greek symbol ? is the population mean.
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If x is a number, then the difference "x - mean" is called its ___.
Deviation.
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Variance
The average of the squares of the deviations (the x - x¯ values for a sample, or the x - ? values for a population).
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How much the statistic varies from one sample to another is known as the ____ _____ of a statistic.
Sampling variability.
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The standard error of the mean.
Measures the sampling variability of a statistic. An example of standard error. It is a special standard deviation and is known as the standard deviation of the sampling distribution of the mean.
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The notation for the standard error of the mean is ?/?n
Where ? is the standard deviation of the population and n is the size of the sample.
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If you add the deviations, the sum is always ____.
Zero.
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By squaring the deviations, you make them positive numbers, and the sum will also be ____.