Question

Variance The 20 subjects used in Data Set 8 “IQ and Brain Size” in Appendix B have weights with a standard deviation of 20.0414 kg. What is the variance of their weights? Be sure to include the appropriate units with the result.

Short answer

The variance of the weights of the 20 twins is equal to 401.6577${\text{kg}}^{\text{2}}$.

Step-by-step solution

Given information

The weights (in kilograms) of 20 identical twins are provided. The value of the standard deviation is equal to 20.0414 kg.

Compute the variance

The variance is a measure that depicts the amount of spread of the values from their mean. By computing the square root of the variance, the standard deviation is obtained.

The unit of varianceis the square of the units of the variable in the dataset.

Thus, by squaring the standard deviation equal to 20.0414 kilograms, the value of the variance is obtained as shown below:

$$\begin{gathered} \text{Variance}=20.{0414}^2 \\ =401.6577 \end{gathered}$$

Therefore, the variance of the weights is equal to 401.6577 ${\text{kg}}^{\text{2}}$.