Question

σ² = (87 - 78)² + (46 - 78)² + (90 - 78)² + (78 - 78)² + (89 - 78)²/5
= (9)² - (32)² + (12)² + (0)² + (11)²/5
= 81 - 1,024 + 144 + 0 + 121/5
= (-678)/5
= -135.6
what is the first error she made in computing the variance?
○ emi failed to find the difference of 89 - 78 correctly.
○ emi divided by n - 1 instead of n.
○ emi evaluated (46 - 78)² as -(32)².
○ emi forgot to take the square root of -135.6.

Explanation:

To identify the first error, we analyze each step:

1. For \((46 - 78)^2\): \(46-78=-32\), and squaring a number \((-32)^2 = 32^2=1024\), not \(-(32)^2\) (since squaring a negative gives a positive).
2. Checking other options:

• \(89 - 78 = 11\) (correct, so first option is wrong).
• The problem is about variance calculation (not standard deviation yet), so the square - root step (fourth option) is not the first error.
• The denominator (second option) is not the first error as the first error is in the squaring step.

So the first error is evaluating \((46 - 78)^2\) as \(-(32)^2\).

Answer:

Emi evaluated \((46 - 78)^2\) as \(-(32)^2\).