# Deviation

Pronunciation: /ˌdi.viˈeɪ.ʃən/ Explain

 Click on the blue points and drag them to change the figure. What would cause the deviations to all be zero? Manipulative 1 - Deviation Created with GeoGebra.

A deviation is the directed distance from each data value of a dataset to the mean of the dataset. To find the deviation of a data element, subtract the mean from the value of the data element. The difference is the deviation. If the deviation is positive, the value of the data element is larger than the mean. If the deviation is negative, the value of the data element is smaller than the mean.

The absolute deviation of a data element is the positive distance between the value of the data value and the mean of the dataset. The absolute deviation is found by taking the absolute value of the deviation.

The average absolute deviation of a dataset is the arithmetic mean of the absolute deviation of all members of the dataset. To find the average absolute deviation of a dataset, add up the absolute deviations of all members of the dataset, then divide by the number of members in the dataset. An average absolute deviation is also called a mean absolute deviation or a mean absolute residual.

The variance of a dataset is the arithmetic mean of the squares of the deviations of the members of the dataset. To find the variance of a dataset, square each deviation (multiply the deviation by itself), add all the squares of the deviations together, then divide by the number of elements of the dataset. The standard deviation of a dataset is the square root of the variance.

Deviation
Data ValueDeviationAbsolute
Deviation
VarianceStandard
Deviation
12-1.581.582.51
140.420.420.17
13-0.580.580.34
10-3.583.5812.84
140.420.420.17
162.422.425.84
151.421.422.01
9-4.584.5821.01
11-2.582.586.67
140.420.420.17
184.424.4219.51
173.423.4211.67
13.582.156.912.63
Table 1: Deviations of a sample dataset

1. McAdams, David E.. All Math Words Dictionary, deviation. 2nd Classroom edition 20150108-4799968. pg 59. Life is a Story Problem LLC. January 8, 2015. Buy the book

McAdams, David E. Deviation. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/deviation.html.

### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)