The two-moving mean for time period 5 with centring is closest to:

Question

BlackTom AI · Accepted Answer

To tackle this question, I first identify what is meant by a two-moving mean with centering in the given context. Here, the phrase suggests using a moving average with a window of size 2 and centering it around the later time point (i.e., the average is taken around the midpoint of the two observations).

Option a: 3.6. This value would correspond to averaging numbers that are not directly adjacent in the data, or it might come from misplacing the window. If we strictly use a two-point centered window, the natural averages are derived from pairs of consecutive values, so 3.6 does not align with any centered two-point calculation from the provided data.

Option b: 3.9. This matches the centered two-point moving average computed at time period 5, using the two surrounding observations at times 4 and 5: (2.7 + 5.1) / 2 = 3.9. This is a clean, exact average of the two values around period 5.

Option c: 4.0. While close to 3.9, 4.0 would imply a rounding or a different pairing that doesn’t correspond to the precise two-point centered calculation with the given data. It’s not the exact mean of any centered two-point window here.

Option d: 4.2. This would require a different pairing or a longer window than 2, or a misapplication of centering. With a two-point centered approach on the provided data, 4.2 does not arise from the relevant neighboring values.

In summary, the only value that correctly arises from a centered two-point moving average using the data around time period 5 is 3.9, calculated from (2.7 at time 4 and 5.1 at time 5) divided by 2. The other options do not correspond to this specific calculation and reflect either misinterpretation or rounding that doesn’t apply here.

The two-moving mean for time period 5 with centring is closest to:

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