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?

1.8 pounds; on average, weight of a bag varies 1.8 pounds from the mean of 7 pounds
1.3 pounds; on average, weight of a bag varies 1.3 pounds from the mean of 7 pounds
1.3 pounds; the weight of 50% of the bags is greater than 1.3 pounds
1.8 pounds; the weight of 50% of the bags is greater than 1.8 pounds

Answer 1

The mean absolute deviation of the weights of the bags is 1.3 pounds, indicating that on average, the weight of a bag varies by 1.3 pounds from the mean weight of 7 pounds.

Step-by-step explanation:

The mean absolute deviation (MAD) represents how much the weights of the bags vary, on average, from the mean (average) weight of the bags. To calculate the MAD, we first find the mean weight of the six bags: (6 + 4 + 8 + 7 + 8 + 9) / 6 = 42 / 6 = 7 pounds. Next, we calculate the absolute deviations from this mean: |6 - 7| + |4 - 7| + |8 - 7| + |7 - 7| + |8 - 7| + |9 - 7| = 1 + 3 + 1 + 0 + 1 + 2 = 8. Finally, we divide the sum of the absolute deviations by the number of bags to find the MAD: 8 / 6 ≈ 1.33 pounds.

Therefore, the correct option is: 1.3 pounds; on average, the weight of a bag varies 1.3 pounds from the mean of 7 pounds. The MAD indicates the average distance between each data point (the weight of each bag) and the mean weight, helping to understand the variability among the weights of the bags.