To calculate the variance of the weights, we use the relationship between standard deviation and variance. The variance ($\sigma^2$) is simply the square of the standard deviation ($\sigma$).

Given:

• Standard deviation $\sigma = 12.4397$ kg

The variance is: $\text{Variance} = \sigma^2 = (12.4397)^2$

Now, let's compute that:

$\text{Variance} = 154.6767 \, \text{kg}^2$

Thus, the variance of the sample data is $154.6767 \, \text{kg}^2$, rounded to four decimal places.

Would you like more details on how variance and standard deviation are related or need further clarification?

Here are 5 related questions you might find helpful:

1. What is the formula for variance and how does it differ from standard deviation?
2. How does sample size affect variance and standard deviation?
3. What are some real-world examples where understanding variance is useful?
4. How do you interpret variance in the context of weight data?
5. Can you explain the difference between population variance and sample variance?

Tip: Always double-check whether you're working with a sample or population, as the formulas for variance slightly differ.