Question

given that the variance of life expectancies was 83.06 squared years, which of the following is the correct standard deviation and units?
√83.06 = 9.1 squared years
√83.06 = 9.1 years
83.06² = 6899 years
83.06² = 6899 squared years
83.06/(201 - 1)=0.4153 years

Explanation:

Step1: Recall standard - deviation formula

The standard deviation $\sigma$ is the square - root of the variance $\sigma^{2}$. That is, $\sigma=\sqrt{\sigma^{2}}$.

Step2: Calculate standard deviation

Given $\sigma^{2} = 83.06$ squared years, then $\sigma=\sqrt{83.06}\approx9.1$ years. The units of variance are squared units of the original variable, and the units of standard deviation are the same as the original variable (years in this case for life - expectancies).

Answer:

$\sqrt{83.06}=9.1$ years