The first error Emi made in computing the Variance is that she evaluated [tex]\((46 - 78)^2\)[/tex] as [tex]\(-(32)^2\)[/tex] instead of correctly evaluating it as [tex]\(32^2\)[/tex].
We can deduce this from the given correct squared differences [tex]\((87 - 78)^2, (46 - 78)^2, (90 - 78)^2, (78 - 78)^2, (89 - 78)^2\)[/tex], and their respective values: [tex]\[81, 1024, 144, 0, 121\][/tex]. The error was specifically in evaluating the second term, [tex]\((46 - 78)^2\)[/tex], where [tex]\((32)^2\)[/tex] should result in [tex]\(1024\)[/tex].
Therefore, the correct answer is:
Emi evaluated [tex]\((46-78)^2\)[/tex] as [tex]\(-(32)^2\)[/tex] instead of [tex]\(32^2\)[/tex].
