The four-moving mean for time period 4 with centring is closest to:

Question

BlackTom AI · Accepted Answer

To tackle the question, we first identify the data values for the period range provided: Time period 1 through 6 have data values [2.3, 3.4, 4.4, 2.7, 5.1, 3.7].

For a four-point moving average with centering, the centered window includes two observations on each side of the central period. This means that the centered 4-point mean at time t uses the values at t-1, t, t+1, and t+2. Consequently, valid centered means exist for time periods t = 2, 3, and 4 (since t+2 must be within 1..6).

Compute each:
- At time period 2: average of periods 1–4 -> (2.3 + 3.4 + 4.4 + 2.7) = 12.8; 12.8 / 4 = 3.2.
- At time period 3: average of periods 2–5 -> (3.4 + 4.4 + 2.7 + 5.1) = 15.6; 15.6 / 4 = 3.9.
- At time period 4: average of periods 3–6 -> (4.4 + 2.7 + 5.1 + 3.7) = 15.9; 15.9 / 4 = 3.975.

Now, compare the computed centered means to the provided options: 3.2, 3.9, and 3.975 correspond to time periods 2, 3, and 4 respectively. The value closest to the centered mean for time period 4 (which is 3.975) is found by looking at the options:
- Option a (2.7) is far from the computed values.
- Option b (4.1) is slightly above 3.975 and not the closest; the difference is about 0.125.
- Option c (3.6) is also farther from 3.975 than 3.9 is.
- Option d (3.9) is very close to 3.9 for time period 3 and is reasonably close to 3.975 as well, making it the closest option among those listed when considering typical rounding in exam contexts.

In summary, the centered four-point mean values are 3.2 (t=2), 3.9 (t=3), and 3.975 (t=4). Among the given choices, 3.9 is the closest match to the centered mean for time period 4 when rounded to one decimal place, aligning with typical reporting in options.

The four-moving mean for time period 4 with centring is closest to:

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