Question

The question.."alex's favorite music album contains nine songs. The length of the songs, in minutes, are shown below."3.4, 4.0, 4.1, 3.5, 3.4, 5.2, 3.8, 2.3, 4.4"what is the mean absolute deviation of the song lengths to the nearest hundredth of a minute"

Answer 1

Given the values of song lengths, in minutes

`\mleft\lbrace3.4,4.0,4.1,3.5,3.4,5.2,3.8,2.3,4.4\}\mright?`

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:

`\text{MAD}=(\Sigma|xi-X\lbrack bar\rbrack|)/(n)`

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:

`X\lbrack bar\rbrack=(\Sigma xi)/(n)`

The number of observations is n=9 songs

You can calculate the sample mean as follows:

`\begin{gathered} X\lbrack bar\rbrack=(3.4+4.0+4.1+3.5+3.4+5.2+3.8+2.3+4.4)/(9) \\ X\lbrack bar\rbrack=(34.1)/(9) \\ X\lbrack bar\rbrack=3.78 \end{gathered}`

Once you have determined the sample mean, you can proceed to calculate the mean absolute deviation:

The mean absolute deviation is 0.57 minutes