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# Absolute Value

## Absolute value is simply the distance from zero of any given number or integer. Check out our modules and lessons below.

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Deviation

Credit: Laura Guerin
Source: CK-12 Foundation

You’re probably familiar with averages (the center of a data set) and standard deviations (the spread of a data set). But how about the mean absolute deviation? It’s another handy statistical tool that has many practical uses.

#### Why It Matters

Consider two schools whose students have the same average SAT score. Does that mean students across the two schools have the same scores? Not necessarily. If three students score 1990, 2000, and 2010, their mean score is 2000. But three students with scores 1900, 2000 and 2100 will also have a mean score of 2000.

Credit: Albeiro Rodas
Source: http://commons.wikimedia.org/wiki/File:Donboscocambodia0001.JPG

It’s clear that the second group has greater deviation among their scores, but how do you distinguish this? How do you measure deviation? You can look at the absolute value of each data point’s difference from the mean. The score 1990 is |20001990|=10\begin{align*}|2000 - 1990|=10\end{align*} points away from the mean, 2010 is |20002010|=10\begin{align*}|2000 - 2010|=10\end{align*} points away, and 2000 is 0 points away. The mean of these absolute deviations is 10+0+103=6.67\begin{align*}\frac{10+0+10}{3}=6.67\end{align*}. For the second data set, this mean absolute deviation comes out to be 66.7, which is 10 times higher than the first mean absolute deviation. By looking at the mean absolute deviation you can tell how “dispersed” the scores of each of the two schools are. Like standard deviation, mean absolute deviation is another measure of spread in a data set.

#### Explore More

Consider two small companies, each of which is staffed by four employees with similar qualifications and responsibilities. For Company A, the employees’ monthly salaries are $3000,$3100, $3100 and$3200. Company B pays salaries of $2600,$3000, $3300 and$3500. Which company treats their employees more fairly? Which one would you work for?

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