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

Question

BlackTom AI · Accepted Answer

For an even-length moving average (4), centring is done by first computing consecutive 4-period moving averages, then averaging adjacent 4-period MAs so the smoothed value falls on an integer time period.

Relevant concepts:
- A 4-period moving average for a window is the simple average of the four observations in that window.
- Because a 4-period MA is centered between the 2nd and 3rd observation of the window (a half-period offset), you must average adjacent 4-period MAs to obtain a centred value at an integer period.

Step-by-step calculation:
1. Compute the 4-period MA for periods 1–4:
   Sum = 2.3 + 3.4 + 4.4 + 2.7 = 12.8
   MA(1–4) = 12.8 / 4 = 3.20  (this is centred at time 2.5)

2. Compute the 4-period MA for periods 2–5:
   Sum = 3.4 + 4.4 + 2.7 + 5.1 = 15.6
   MA(2–5) = 15.6 / 4 = 3.90  (centred at time 3.5)

3. Compute the 4-period MA for periods 3–6:
   Sum = 4.4 + 2.7 + 5.1 + 3.7 = 15.9
   MA(3–6) = 15.9 / 4 = 3.975 (centred at time 4.5)

4. To centre the moving average at time period 4 (an integer), average the two adjacent centred MAs at 3.5 and 4.5:
   Centre MA at time 4 = (MA(2–5) + MA(3–6)) / 2
                     = (3.90 + 3.975) / 2
                     = 7.875 / 2 = 3.9375 ≈ 3.94

Why this is correct:
- The computed centred 4-period MA at time 4 is approximately 3.9375, which rounds to 3.9. This follows the standard procedure for centring even-length moving averages.

Why the other choices are incorrect:
- 4.1 is higher than the correctly computed 3.9375 and does not match the averaging result.
- 3.6 is too low compared with the calculated value of about 3.94.
- 2.7 is merely one raw data point (time 4 value) and not the centred 4-period moving average.

Conclusion: The centred four-moving mean for time period 4 is closest to 3.9, so the correct answer is c. 3.9.

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