Question

The following data shows the weight, in pounds, of 6 bags: 6, 4, 8, 7, 8, 9 What is the value of the mean absolute deviation of the weight of the bags, and what does it represent about the weight of a bag?

Answer 1

Answer:

$MAD = 1.333$ Pounds

Step-by-step explanation:

The first step is to find the , mean of the data 6, 4, 8, 7, 8, 9

$\mu= \frac{6 + 4 + 8 + 7 + 8 + 9}{6}\\\\\mu = 7$

Now we find the difference between each data $x_i$ and the mean . $|\mu-x_i|$

$| 7-6 | = 1\\\\| 7-4 | = 3\\\\| 7-8 | = 1\\\\| 7-7 | = 0\\\\| 7-8 | = 1\\\\| 7-9 | = 2$

Now we add all the difference and then we divide the result between the data number $n=6$:

$MAD = \frac{1 + 3+ 1 + 0 +1 +2}{6}$

$MAD = 1.333$ Pounds

This value means that the average difference between the weight of each bag and the average weight of the bags is 1,333 pounds.

The mean deviation represents a measure of how scattered the data are with respect to the mean. That is, the DMA measures how much the weight of a bag differs from the average weight of the 6 bags