The three-moving mean for time period 2 is closest to:

Question

BlackTom AI · Accepted Answer

A three-period centered moving mean at time 2 equals the average of the observations for periods 1, 2 and 3.

1) Relevant knowledge points and concepts
- A k-period moving mean (here k = 3) smooths a time series by averaging k consecutive observations.
- For a centered 3-period moving mean assigned to time t = 2, use the values at periods 1, 2, and 3.

2) Complete reasoning process step by step
- Identify the three observations to average: period 1 = 2.3, period 2 = 3.4, period 3 = 4.4.
- Sum these three observations and divide by 3 to get the 3-period moving mean for time 2.

3) Calculations (all intermediate steps)
- Sum: 2.3 + 3.4 = 5.7
- Add third value: 5.7 + 4.4 = 10.1
- Average: 10.1 / 3 = 3.366666... ≈ 3.37
- Rounded to one decimal place (to compare with the choices): 3.4

4) Why the correct answer is correct
- The computed three-period moving mean (3.3667) is closest to 3.4 among the given options. This value directly follows from the standard definition of a 3-period moving average using periods 1–3 for time 2.

5) Why the other options are incorrect
- b. 4.0 is 0.6333 away from the computed mean, considerably farther than 3.4.
- c. 3.6 is 0.2333 away, closer than 4.0 but still farther than 3.4 (0.0333 difference).
- d. 3.9 is 0.5333 away, also farther away than 3.4.
- Therefore none of b, c, or d match the calculated average as closely as 3.4.

6) Conclusion
- The three-moving mean for time period 2 is approximately 3.3667, which rounds to 3.4. This confirms the correct answer is a. 3.4.

The three-moving mean for time period 2 is closest to:单项选择题

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