A moving average transforms a fixed series into exact window averages. This lesson shows the arithmetic window directly, then checks that the plotted values and table values match the recompute.

highlighted = computed this step

Window average

MA(3) averages the last 3 observed values. Motivation: a window average replaces one noisy observation with a local arithmetic summary.

MA3=window sum/3MA_{3}=\text{window sum}/3
MA threeMA threeExact arithmetic mechanics only; no accuracy claimperiodvalue012345673313/3414/3519/36

One window

For period 4, the window values are 4, 3, and 6; their sum is 13. Why: the fraction comes from this exact sum divided by the window length, with no fitted parameter hidden behind the table.

(4+3+6)/3=13/3(4 + 3 + 6)/3=13/3
Moving average exact valuesThe raw row and MA row use the same displayed periods.series and MAt3t4t5t6series3658MA(3)313/314/319/3

All MA values

The MA(3) outputs are 3, 13/3, 14/3, and 19/3. Interpretation: every displayed bar is a recomputed window, so the plot is a visual form of the same exact table.

MA values=3,13/3,14/3,19/3\text{MA values}=3,13/3,14/3,19/3
Moving average exact valuesThe raw row and MA row use the same displayed periods.series and MAt3t4t5t6series3658MA(3)313/314/319/3

Diagram note

Honesty note: These values are exact formula outputs on the pinned integer series; they do not validate what happens later. Pixel positions are rounded for layout; every number shown is exact.

moving-average outputs are exact window arithmetic\text{moving-average outputs are exact window arithmetic}
Moving average exact valuesThe raw row and MA row use the same displayed periods.series and MAt3t4t5t6series3658MA(3)313/314/319/3