Respuesta :
Given the values of song lengths, in minutes
[tex]\mleft\lbrace3.4,4.0,4.1,3.5,3.4,5.2,3.8,2.3,4.4\}\mright?[/tex]To calculate the mean absolute deviation (MAD) of the lengths of the songs you have to calculate the absolute difference between each value and the sample mean, add all results, and divide it by the sample size, following the formula:
[tex]\text{MAD}=\frac{\Sigma|xi-X\lbrack bar\rbrack|}{n}[/tex]Where
MAD is the mean absolute deviation
xi is each observation of the sample
X[bar] is the sample mean
n is the sample size
The first step is to calculate the sample mean:
To do so you have to add all values and divide them by the number of observations:
[tex]X\lbrack bar\rbrack=\frac{\Sigma xi}{n}[/tex]The number of observations is n=9 songs
You can calculate the sample mean as follows:
[tex]\begin{gathered} X\lbrack bar\rbrack=\frac{3.4+4.0+4.1+3.5+3.4+5.2+3.8+2.3+4.4}{9} \\ X\lbrack bar\rbrack=\frac{34.1}{9} \\ X\lbrack bar\rbrack=3.78 \end{gathered}[/tex]Once you have determined the sample mean, you can proceed to calculate the mean absolute deviation:
[tex]\begin{gathered} \text{MAD}=\frac{|3.4-3.78|+|4.0-3.78|+|4.1-3.78|+|3.5-3.78|+|3.4-3.78|+|5.2-3.78|+|3.8-3.78|+|2.3-3.78|+|4.4-3.78|}{9} \\ \text{MAD}=\frac{0.38+0.22+0.32+0.28+0.38+1.42+0.02+1.48+0.62}{9} \\ \text{MAD}=\frac{5.12}{9} \\ \text{MAD}=0.57 \end{gathered}[/tex]The mean absolute deviation is 0.57 minutes
