Question

What is the mean and mad of this data set?

Answer 1

Answer:

The mean number of gerbils seen per day is 6.

The mean absolute deviation of the data is 2.29.

Step-by-step explanation:

The mean of a data set is the value that represents the entire data set. It is the average value.

The formula to compute the mean of a data set is:

$\bar x=\frac{1}{n}\sum X$

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:

$MAD=\frac{1}{n}\sum |x-\bar x|$

The data set for the number of gerbils seen per day is:

S = {2, 3, 5, 7, 8, 8, 9}

Compute the mean of the data as follows:

$\bar x=\frac{1}{n}\sum X$

  $=\frac{1}{7}\times [2+3+5+7+8+8+9]\\\\=\frac{1}{7}\times 42\\\\=6$

The mean number of gerbils seen per day is 6.

Compute the mean absolute deviation of the data as follows:

$MAD=\frac{1}{n}\sum |x-\bar x|$

          $=\frac{1}{7}\times [|2-6|+|3-6|+|5-6|+|7-6|+|8-6|+|8-6|+|9-6|]\\\\=\frac{1}{7}\times 16\\\\=2.2857\\\\\approx 2.29$

Thus, the mean absolute deviation of the data is 2.29.