We have to calculate the mean absolute deviation (MAD) for these temperatures.
We can express the MAD as:
[tex]\text{MAD}=\frac{1}{n}\sum ^n_{i=1}|x_i-\bar{x|}[/tex]
So first we have to calculate the mean of the sample. We can do this as:
[tex]\bar{x}=\frac{1}{n}\sum ^n_{i=1}x_i=\frac{1}{6}(103+110+112+109+105+103)=\frac{1}{6}\cdot642=107[/tex]
Now we can calculate the MAD as:
[tex]\begin{gathered} \text{MAD}=\frac{1}{6}(|103-107|+|110-107|+|112-107|+|109-107|+|105-107|+|103-107|) \\ MAD=\frac{1}{6}(4+3+5+2+2+4) \\ \text{MAD}=\frac{1}{6}(20) \\ \text{MAD}\approx3.3 \end{gathered}[/tex]
Answer: The MAD is approximately 3.3.
