Question

a random sample of 10 subjects have weights with a standard deviation of 10.2933 kg. what is the variance of their weights? be sure to include the appropriate units with the result. the variance of the sample data is (round to four decimal places as needed) units: kg², kg, kg³

Explanation:

Step1: Recall the relationship between variance and standard deviation

The variance ($s^2$) is the square of the standard deviation ($s$). So the formula is $s^2=(s)^2$.

Step2: Substitute the given standard deviation into the formula

Given $s = 10.2933\space kg$, then $s^2=(10.2933)^2$.
Calculate $10.2933\times10.2933 = 105.95202489$.

Step3: Round to four decimal places

Rounding $105.95202489$ to four decimal places gives $105.9520$. The unit for variance is the square of the unit of the data, so it is $kg^2$.

Answer:

$105.9520\space kg^2$