What Is a Worked Example of SMA? (Simple, Verifiable Calculation)

Direct answer

A worked example of SMA (Simple Moving Average) is a step-by-step calculation where you pick a window size N, list the input values, and compute the average of the most recent N values at each point.

A key requirement for a verifiable example is that every assumption is stated: the window size, the exact input numbers, and how “at each step” is aligned to the data you’re averaging.

Mechanism or definition

SMA stands for Simple Moving Average. “Simple” means it uses an unweighted arithmetic mean (all N values count equally).

Definition (discrete time): if you have a series of values (x_1, x_2, \dots), then the SMA with window size N at time t (where (t \ge N)) is: [ \text{SMA}t = \frac{x{t-N+1}+x_{t-N+2}+\dots+x_t}{N} ] Assumptions you must make explicit in any worked example:

1. The window size N (how many recent values are averaged).
2. The exact input sequence (x_t).
3. The alignment rule (SMA_t uses values ending at t, so it is “based on” the last N values including the current one).

Evidence or example

Worked numerical example with all assumptions stated.

Assumptions:

• Window size: N = 3.
• Input values (in the order they occur):
  • x1 = 10
  • x2 = 12
  • x3 = 14
  • x4 = 13
  • x5 = 15
• Alignment: SMA is computed at each time t ≥ 3 using the last 3 values ending at t.

Calculations:

• SMA3 = (x1 + x2 + x3) / 3 = (10 + 12 + 14) / 3 = 36/3 = 12
• SMA4 = (x2 + x3 + x4) / 3 = (12 + 14 + 13) / 3 = 39/3 = 13
• SMA5 = (x3 + x4 + x5) / 3 = (14 + 13 + 15) / 3 = 42/3 = 14

Material limitation shown by this example’s mechanics:

• The SMA starts only when there are at least N values (here, at t=3). Earlier points have no defined SMA unless you add a rule (for example, padding or using smaller windows). Any such rule changes results.

Limitations and risks

SMA is a mathematical transform of past data, not a guarantee of future movement.

Common limitations to understand before using SMA in any analysis:

• Lag (delay): because SMA averages the last N values, it generally reacts more slowly than the newest value. With N=3, any change must appear across several points to strongly move the average.
• Window sensitivity: different N values produce different SMA paths. A short N tracks changes faster; a long N smooths more but can hide turning points.
• Data and preprocessing dependency: SMA results depend on exactly what you average (e.g., raw values vs. adjusted values) and how missing data or irregular sampling is handled.
• Failure mode during regime changes: when the underlying pattern in the input series shifts abruptly, a moving average can remain “in between” states because it reflects a blend of old and new values.
• Historical non-persistence: even if SMA behavior matched past patterns in your chosen data, it does not establish that the same relationship will repeat.

Verification or next question

You can independently verify the worked example by recomputing SMA using the same stated assumptions (N=3, the exact input values 10, 12, 14, 13, 15, and the alignment that SMA_t uses the last N values ending at t).

A next useful question is: what window size N changes the smoothness and lag for your specific dataset? Any answer should still state the assumptions (N and the input series) so the calculation remains reproducible.