Answer :
Final answer:
The variance of the crate weights is calculated by first finding the mean weight, then computing the squared differences from the mean for each weight, and finally dividing the sum of these squared differences by the number of data points minus one. The variance for the crate weights is 11 kg^2.
Explanation:
To calculate the variance of the crate weights, first, we need to find the mean (average) weight of the crates. Then we will use this mean to determine the squared differences from the mean for each data point, and finally, we'll find the average of these squared differences.
Step-by-Step Calculation:
- Calculate the mean weight: (103 + 97 + 101 + 106 + 103) / 5 = 102 kg.
- Calculate the squared differences from the mean: (103-102)^2, (97-102)^2, (101-102)^2, (106-102)^2, (103-102)^2.
- Sum the squared differences: 1^2 + 5^2 + 1^2 + 4^2 + 1^2 = 1 + 25 + 1 + 16 + 1 = 44.
- Divide the sum of squared differences by the number of data points (n-1 for a sample variance), which is 5-1 = 4: 44 / 4 = 11 kg^2.
The variance of the weights of the crates is 11 kg^2.
