what is the first error she made in computing the variance?\nemi failed to find the difference of 89 - 78…

Explanation:

Step1: Recall variance - calculation rule

The formula for the population variance $\sigma^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\mu)^{2}}{n}$, where $x_{i}$ are data - points and $\mu$ is the mean, and $n$ is the number of data - points. When calculating $(a - b)^{2}$, we have $(a - b)^{2}=(b - a)^{2}=a^{2}-2ab + b^{2}$, and it is always non - negative.

Step2: Analyze the error

In the step $\frac{(9)^{2}-(32)^{2}+(12)^{2}+(0)^{2}+(11)^{2}}{5}$, the error occurs when evaluating $(46 - 78)^{2}$. Since $(46 - 78)^{2}=(-32)^{2}=32^{2}$, but it was wrongly evaluated as $-(32)^{2}$.

Answer:

Emi evaluated $(46 - 78)^{2}$ as $-(32)^{2}$.