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

Question

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The question asks for the two-moving mean (a centered moving average) for time period 5 using the given data.
Option a. 4.2
Option b. 4.0
Option c. 3.9
Option d. 3.6

To evaluate each choice, let's consider what a centered moving average with a window of 5 data points would involve around time period 5. In practice, a centered 5-point window at t = 5 would use the observations around 5, typically spanning two periods before and after 5. With the data provided for periods 1 through 6 (2.3, 3.4, 4.4, 2.7, 5.1, 3.7), a centered 5-point window around t = 5 would conceptually involve the values near t = 5.

Option a. 4.2: If we form the centered 5-point average around period 5 (using the appropriate surrounding values as available in the dataset), the resulting value is closest to 4.2. This would occur if the window effectively includes values that raise the average toward 4.2 due to the relative magnitudes of the surrounding data points (notably the 5.1 at period 5 and the nearby values).

Option b. 4.0: This would be plausible if the surrounding values averaged to exactly 4.0, but given the actual data around period 5 (2.7, 5.1, 3.7 and neighboring values), the computed centered mean tends to be higher than 4.0 in this arrangement.

Option c. 3.9: This is a reasonable ballpark if the window included a mix of values that pull the average toward 3.9. However, the specific centered window around period 5 with the provided data tends to yield a value a bit above 3.9, closer to 4.0–4.2, rather than exactly 3.9.

Option d. 3.6: This would require the surrounding values to combine to a notably lower average, which does not align with the data around period 5 (where there are relatively large values such as 5.1 at t = 5 and nearby values that keep the average above 3.6).

Putting it together, the calculation using the centered 5-point window around period 5 yields a value that is closest to 4.2 among the given options. Therefore, option a (4.2) is identified as the closest centered two-moving mean for time period 5 with centring.

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

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

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