# How do you find the mean absolute deviation for the numbers 69, 78, 80, 88, 88, 88, 88, 101, 102, and 108?

Jul 13, 2018

$\text{Mean Absolute Deviation } = \frac{88}{10} = 8.8$

#### Explanation:

We know that ,
color(red)("Mean Absolute Deviation " = (sum|x_i-barX|)/N

$W h e r e , {x}_{i} = \text{data value" and sumx_i="sum of data values}$

color(blue)(barX=(sumx_i)/N=Mean

$N = \text{Number of values}$

color(green)(|x_i-barX|="Absolute deviation"

Here ,

${x}_{i} : 69 , 78 , 80 , 88 , 88 , 88 , 88 , 101 , 102 , 108$

$\implies \sum {x}_{I} = 890 \mathmr{and} N = 10$

=>color(blue)(barX=890/10=89

${x}_{i} - \overline{X} = - 20 , - 11 , - 9 , - 1 , - 1 , - 1 , - 1 , 12 , 13 , 19$

color(green)(|x_i-barX|=20,11,9,1,1,1,1,12,13,19

$\sum | {x}_{i} - \overline{X} | = 88$

So,
color(red)("Mean Absolute Deviation "=88/10=8.8