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[tex]\[
\begin{array}{l}
\sigma^2 = \frac{(87-78)^2+(46-78)^2+(90-78)^2+(78-78)^2+(89-78)^2}{5} \\
= \frac{(9)^2 + (-32)^2 + (12)^2 + (0)^2 + (11)^2}{5} \\
= \frac{81 + 1024 + 144 + 0 + 121}{5} \\
= \frac{1370}{5} \\
= 274
\end{array}
\][/tex]

What is the first error she made in computing the variance?

A. Emi failed to find the difference of 89 - 78 correctly.
B. Emi divided by [tex]\( N-1 \)[/tex] instead of [tex]\( N \)[/tex].
C. Emi evaluated [tex]\( (46-78)^2 \)[/tex] as [tex]\( -(32)^2 \)[/tex].
D. Emi forgot to take the square root of -135.6.



Answer :

GinnyAnswer
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].

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