Respuesta :
Answer:
The number of miles biked each day by the bicyclists varied by an average of 4 miles from the mean.
Step-by-step explanation:
The mean absolute deviation (MAD) of a data set is the average distance amid each value and the mean. The MAD provides us with an idea about the deviation in the data-set.
The formula to calculate the value of MAD is,
[tex]\tex{MAD}=\frac{1}{n}\sum\limits^{n}_{i=1}{|x_{i}-\bar x|}[/tex]
The data is:
S = {7, 10, 13, 4, 12, 21, 10, 3}
Compute the mean of the data as follows:
[tex]\bar x=\frac{1}{n}\sum\limits^{n}_{i=1}{x_{i}}\\\\=\frac{1}{8} [7+10+13+4+12+21+10+3]\\\\=10[/tex]
Compute the value of MAD as follows:
[tex]\tex{MAD}=\frac{1}{n}\sum\limits^{n}_{i=1}{|x_{i}-\bar x|}[/tex]
[tex]=\frac{1}{8}\times [|7-10|+|10-10|+|13-10|+...+|3-10|]\\\\=\frac{32}{8}\\\\=4[/tex]
Thus, the mean absolute deviation is 4.
The number of miles biked each day by the bicyclists varied by an average of 4 miles from the mean.
