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where #ofSTDEVs = the number of standard deviations.

In general, a va lue = mean + (#ofSTDEV)(standard deviation).

If one were also part of the data set, then one is two standard deviations to the left of five because 5 + (–2)(2) = 1. One standard deviation to the right of five because 5 + (1)(2) = 7. If we were to put five and seven on a number line, seven is to the right of five. The number line may help you understand standard deviation. (You will learn more about this in later chapters.) In general, the shape of the distribution of the data affects how much of the data is further away than two standard deviations.

Considering data to be far from the mean if it is more than two standard deviations away is more of an approximate “rule of thumb” than a rigid rule. Binh’s wait time of one minute is two standard deviations below the average of five minutes.Ī data value that is two standard deviations from the average is just on the borderline for what many statisticians would consider to be far from the average.Binh’s wait time of one minute is four minutes less than the average of five minutes.One is four minutes less than the average of five four minutes is equal to two standard deviations.Rosa’s wait time of seven minutes is one standard deviation above the average of five minutes.Rosa’s wait time of seven minutes is two minutes longer than the average of five minutes.Seven is two minutes longer than the average of five two minutes is equal to one standard deviation.The standard deviation can be used to determine whether a data value is close to or far from the mean. At supermarket A, the mean waiting time is five minutes and the standard deviation is two minutes. Rosa waits at the checkout counter for seven minutes and Binh waits for one minute. Suppose that Rosa and Binh both shop at supermarket A. Overall, wait times at supermarket B are more spread out from the average wait times at supermarket A are more concentrated near the average. At supermarket A, the standard deviation for the wait time is two minutes at supermarket B the standard deviation for the wait time is four minutes.īecause supermarket B has a higher standard deviation, we know that there is more variation in the wait times at supermarket B. the average wait time at both supermarkets is five minutes. Suppose that we are studying the amount of time customers wait in line at the checkout at supermarket A and supermarket B. The standard deviation is larger when the data values are more spread out from the mean, exhibiting more variation. The standard deviation is small when the data are all concentrated close to the mean, exhibiting little variation or spread.

The standard deviation is always positive or zero. The standard deviation provides a measure of the overall variation in a data set. The standard deviation 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. The standard deviation is a number that measures how far data values are from their mean. The most common measure of variation, or spread, is the standard deviation. In some data sets, the data values are concentrated closely near the mean in other data sets, the data values are more widely spread out from the mean. Recognize, describe, and calculate the measures of the spread of data: variance, standard deviation, and range.Īn important characteristic of any set of data is the variation in the data.If you install SAS Business Rules Manager 3.3 as an upgrade, you might observe that the SAS Business Rules Manager displays existing rules without an equal sign, as shown in the following example:Ĭlick the Hot Fix tab in this note to access the hot fix for this issue.