Question

Vivian surveyed bicyclists in her community to see the average number of miles they biked per day. Her results are shown below. 7, 10, 13, 4, 12, 21, 10, 3 What is the MAD of her data set? What does this tell you about the number of miles biked each day by the bicyclists? The mean of the data set is . The MAD of the data set is . So, the number of miles biked each day by the bicyclists varied by an average of miles from the mean.

Answer 1

The number of miles biked each day by the bicyclists varied by an average of 4 miles from the mean.

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{MAD}=(1)/(n)\sum\limits^(n)_(i=1)x_(i)-\bar x`

The data is:

S = {7, 10, 13, 4, 12, 21, 10, 3}

Compute the mean of the data as follows:

`\bar x=(1)/(n)\sum\limits^(n)_(i=1){x_(i)}\\\\=(1)/(8) [7+10+13+4+12+21+10+3]\\\\=10`

Compute the value of MAD as follows:

`\tex{MAD}=(1)/(n)\sum\limits^(n)_(i=1)`

`=(1)/(8)* [|7-10|+|10-10|+|13-10|+...+|3-10|]\\\\=(32)/(8)\\\\=4`

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.