The variance is simply the square of the standard deviation. Since you're given the standard deviation of 12.1768 kg, the variance can be calculated as follows:

$\text{Variance} = (\text{Standard Deviation})^2 = (12.1768)^2$

$\text{Variance} = 148.26 \, \text{kg}^2$

Thus, the variance of the weights is 148.26 kg².

Would you like to see further steps or explanations? Let me know if you need more details!

Follow-up Questions:

1. How does the concept of variance differ from standard deviation?
2. How can variance and standard deviation be used to interpret data in a practical scenario?
3. If the sample size increased, how would that affect the variance and standard deviation?
4. How would you calculate the variance if you had the entire population data instead of a sample?
5. What does the unit "kg²" tell us in terms of variability?

Tip: Variance can sometimes be hard to interpret directly, as it is in squared units. Standard deviation is often preferred because it is in the same units as the original data.