# Standard Deviation

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 Standard DeviationA measure of dispersion for interval variables.(Manheim, J.B., Richard, C.R., Willnat, L., & Brians, C.L. (2008). Empirical political analysis: Quantitative and qualitative research methods (7th ed.). New York: Pearson.)------------------------Standard deviation is the measure of spread most commonly used in statistical practice when the mean is used to calculate central tendency. Thus, it measures spread around the mean. Because of its close links with the mean, standard deviation can be greatly affected if the mean gives a poor measure of central tendency.Outliers also influence standard deviation; one value could contribute largely to the results of the standard deviation. In that sense, the standard deviation is a good indicator of the presence of outliers. This makes standard deviation a very useful measure of spread for symmetrical distributions with no outliers.Standard deviation is also useful when comparing the spread of two separate data sets that have approximately the same mean. The data set with the smaller standard deviation has a narrower spread of measurements around the mean and therefore usually has comparatively fewer high or low values. An item selected at random from a data set whose standard deviation is low has a better chance of being close to the mean than an item from a data set whose standard deviation is higher.Generally, the more widely spread the values are, the larger the standard deviation is. For example, imagine that we have to separate two different sets of exam results from a class of 30 students; the first exam has marks ranging from 31% to 98%, the other ranges from 82% to 93%. Given these ranges, the standard deviation would be larger for the results of the first exam.ReferencesVariance and standard deviation. Statistics Canada. 20 April 2009, from http://www.statcan.gc.ca/edu/power-pouvoir/ch12/5214891-eng.htm#properties.
Standard Deviation

A measure of dispersion for interval variables.

(Manheim, J.B., Richard, C.R., Willnat, L., & Brians, C.L. (2008). Empirical political analysis: Quantitative and qualitative research methods (7th ed.). New York: Pearson.)

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Standard deviation is the measure of spread most commonly used in statistical practice when the mean is used to calculate central tendency. Thus, it measures spread around the mean. Because of its close links with the mean, standard deviation can be greatly affected if the mean gives a poor measure of central tendency.

Outliers also influence standard deviation; one value could contribute largely to the results of the standard deviation. In that sense, the standard deviation is a good indicator of the presence of outliers. This makes standard deviation a very useful measure of spread for symmetrical distributions with no outliers.

Standard deviation is also useful when comparing the spread of two separate data sets that have approximately the same mean. The data set with the smaller standard deviation has a narrower spread of measurements around the mean and therefore usually has comparatively fewer high or low values. An item selected at random from a data set whose standard deviation is low has a better chance of being close to the mean than an item from a data set whose standard deviation is higher.

Generally, the more widely spread the values are, the larger the standard deviation is. For example, imagine that we have to separate two different sets of exam results from a class of 30 students; the first exam has marks ranging from 31% to 98%, the other ranges from 82% to 93%. Given these ranges, the standard deviation would be larger for the results of the first exam.

References

Variance and standard deviation. Statistics Canada. 20 April 2009, from
http://www.statcan.gc.ca/edu/power-pouvoir/ch12/5214891-eng.htm#properties.

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