Question

The daily wages paid to five workers are $25, $40, $65, $55, and $50. What is the mean absolute deviation of this data set? Round your answer to one decimal point if necessary.

Answer 1

Hello!

The mean is the mean of how close each number is to the mean. To calculate it, first you find the mean of the data set.

(25+40+65+55+50)÷5=47

Now we have to find the absolute value of the distance between each number and the mean. We add all of these up and divide by five to find the mean absolute deviation (note that since we are doing absolute value we do not have to worry about which number comes first).

|47-25 |=22
|47-40 |=7
|47-65 |=18
|47-55 |=8
|47-50 |=3

Now we find the mean of all these values.

(22+7+18+8+3)÷5=11.6

The mean absolute deviation is 11.6.

I hope this helps!

Answer 2

We have a few steps we need to do to find the mean absolute deviation of a set of numbers. First, find the mean. Second, find the distance the numbers are from the mean. Third, average out the distances.

Finding the Mean
To find the mean/average, you add up all the numbers in the set, and divide it by the amount of numbers.
25+40+50+55+65=235
Now divide by 5.
235÷5=47
So, the mean is 47.

Finding the Distances
We can subtract the numbers from the mean, and we can ignore the negatives.
47-25=22
47-40=7
47-65=-18; 18
47-55=-8;8
47-50=-3;3
So, the distances are: 3, 7, 8, 18, and 22.

Finding the Mean of the Distances
Add them up.
3+7+8+18+22=58
Now divide by 5.
58÷5=11.6

So, the mean absolute deviation is 11.6.