Answer :
Final answer:
To find the mean deviation of the crate weights, calculate the mean weight first, which is 102 kg, then the average of the absolute differences between each weight and this mean. The mean deviation is 2.4 kg.
Explanation:
The question concerns finding the mean deviation of a set of weights. First, we calculate the mean (average) weight of the crates, which involves summing all the weights and dividing by the number of crates. The weights given are: 103, 97, 101, 106, and 103 kilograms. The sum of these weights is 510 kilograms. Dividing by the number of weights (5), we find the mean weight to be 102 kilograms.
Next, we calculate the mean deviation. The mean deviation is the average of the absolute differences between each data point and the mean. The deviations from the mean are:
- Absolute deviation for 103 kg = |103 - 102| = 1 kg
- Absolute deviation for 97 kg = |97 - 102| = 5 kg
- Absolute deviation for 101 kg = |101 - 102| = 1 kg
- Absolute deviation for 106 kg = |106 - 102| = 4 kg
- Absolute deviation for 103 kg = |103 - 102| = 1 kg
Adding these absolute deviations gives us 12 kilograms. To find the mean deviation, we divide this sum by the number of weights (5), resulting in a mean deviation of 2.4 kilograms.
