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

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To approach a centered moving average of window size 4, we consider two data points on either side of the center, giving us the values at positions t-1, t, t+1, and t+2 for the centered time t.
Option a. 4.1: If we check the actual calculation for the four-point centered window around time 4, the relevant data values are at times 3, 4, 5, and 6. These are 4.4, 2.7, 5.1, and 3.7 respectively. Their average is (4.4 + 2.7 + 5.1 + 3.7) / 4 = 15.9 / 4 = 3.975, which rounds to about 3.98, closer to 4.0 than to 4.1, so 4.1 is not a close match.
Option b. 3.9: The computed centered four-point average is 3.975. Among the given options, 3.9 is the closest value to 3.975, differing by only 0.075, whereas 4.1, 3.6, and 2.7 are farther away.
Option c. 3.6: This would require the window average to be around 3.6, which would imply a quite different set of four points or a different centering; using the actual data around time 4 yields 3.975, not 3.6.
Option d. 2.7: This is substantially lower than the computed 3.975 and would only be plausible if the window included much smaller numbers than those present around time 4; the actual four-point window around time 4 does not support this value.
In summary, centering a 4-point moving average on time 4 uses the values 4.4, 2.7, 5.1, and 3.7, giving an average of 3.975. The closest option to this value is 3.9, making it the best match among the choices.

MUF0142 Fund. Mathematics Unit 2 - Semester 2, 2025 8.6 Time Series: Smoothing Quiz (Formative)

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

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