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

Question

BlackTom AI · Accepted Answer

Compute the two-period moving averages between adjacent observations, then centre them to obtain a value at an integer time. For period 5 the centred two-moving mean is the average of the 2-period MA for (4,5) and the 2-period MA for (5,6).

1. Relevant knowledge points and concepts
- A 2-period moving average (2-MA) for time t is (x_t + x_{t+1})/2 and lies between t and t+1 (at t+0.5).
- To get a centred value at an integer period when using an even-length MA, average two adjacent 2-MAs. Thus the centred 2-MA at period k is the mean of the 2-MA for (k-1,k) and the 2-MA for (k,k+1).

2. Step-by-step reasoning
- Compute 2-MAs for the relevant adjacent pairs: (4,5) and (5,6).
- Centre by averaging those two 2-MAs to assign the result to period 5.

3. Calculations (all intermediate steps)
- Data values: period 4 = 2.7, period 5 = 5.1, period 6 = 3.7.
- 2-MA for (4,5) = (2.7 + 5.1) / 2 = 7.8 / 2 = 3.9.
- 2-MA for (5,6) = (5.1 + 3.7) / 2 = 8.8 / 2 = 4.4.
- Centred 2-MA at period 5 = (3.9 + 4.4) / 2 = 8.3 / 2 = 4.15 ≈ 4.2.

4. Why the correct answer is correct
- The centred procedure gives 4.15 which rounds to 4.2. This follows directly from averaging the two adjacent 2-period MAs that straddle period 5.

5. Why the other options are incorrect
- a. 3.9 is the uncentred 2-MA for (4,5) only, not the centred value for period 5.
- c. 3.6 does not arise from any correct combination of the adjacent 2-MAs here.
- d. 4.0 is an incorrect rounding of 4.15 (should be 4.2) and is not the computed centred value.

6. Conclusion
- The centred two-moving mean for time period 5 is 4.15, which rounds to 4.2. Therefore the correct choice is b. 4.2.

The two-moving mean for time period 5 with centring is closest to:单项选择题

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