Rolling Mean (Window = 3) - Pandas Step by Step

Compute a 3-element sliding-window average over an ordered numeric sequence. By hand, the first two positions cannot form a full window so they get None; positions 2 onward average the current element and the two before it. With pandas, Series.rolling(3).mean() handles the window and fills the incomplete prefix with NaN.

By hand

Walk range(len(readings)). Indices 0 and 1 have fewer than 3 elements available, so append None. From index 2 onward, slice the 3-element window readings[i - 2: i + 1] into w, compute round(sum(w) / 3, 2), and append. The trace shows w refreshing each iteration alongside the growing result.

                            naive.py
                        
Replay: real traced execution (multi-file project)

                            readings = [6, 9, 12, 9, 15, 9]
result = []
for i in range(len(readings)):
    if i < 2:
        result.append(None)
    else:
        w = readings[i - 2: i + 1]
        result.append(round(sum(w) / 3, 2))
print('RESULT:', result)

                        
1readings ← [6, 9, 12, 9, 15, 9]1readings = [6, 9, 12, 9, 15, 9]2result = []⋯values this step[6, 9, 12, 9, 15, 9]readings
2result ← []1readings = [6, 9, 12, 9, 15, 9]2result = []3for i in range(len(readings)):⋯values this step[]result
3i ← 0⋯2result = []3for i in range(len(readings)):4    if i < 2:⋯values this step0i
4if i < 2:⋯3for i in range(len(readings)):4    if i < 2:5        result.append(None)⋯
5result ← [None]⋯4if i < 2:5    result.append(None)6else:⋯values this step[] → [None]result
6i ← 1⋯2result = []3for i in range(len(readings)):4    if i < 2:⋯values this step0 → 1i
7if i < 2:⋯3for i in range(len(readings)):4    if i < 2:5        result.append(None)⋯
8result ← [None, None]⋯4if i < 2:5    result.append(None)6else:⋯values this step[None] → [None, None]result
9i ← 2⋯2result = []3for i in range(len(readings)):4    if i < 2:⋯values this step1 → 2i
10if i < 2:⋯3for i in range(len(readings)):4    if i < 2:5        result.append(None)⋯
11w ← [6, 9, 12]⋯6else:7    w = readings[i - 2: i + 1]8    result.append(round(sum(w) / 3, 2))⋯values this step[6, 9, 12]w
12result ← [None, None, 9.0]⋯7        w = readings[i - 2: i + 1]8        result.append(round(sum(w) / 3, 2))9print('RESULT:', result)values this step[None, None] → [None, None, 9.0]result
13i ← 3⋯2result = []3for i in range(len(readings)):4    if i < 2:⋯values this step2 → 3i
14if i < 2:⋯3for i in range(len(readings)):4    if i < 2:5        result.append(None)⋯
15w ← [9, 12, 9]⋯6else:7    w = readings[i - 2: i + 1]8    result.append(round(sum(w) / 3, 2))⋯values this step[6, 9, 12] → [9, 12, 9]w
16result ← [None, None, 9.0, 10.0]⋯7        w = readings[i - 2: i + 1]8        result.append(round(sum(w) / 3, 2))9print('RESULT:', result)values this step[None, None, 9.0] → [None, None, 9.0, 10.0]result
17i ← 4⋯2result = []3for i in range(len(readings)):4    if i < 2:⋯values this step3 → 4i
18if i < 2:⋯3for i in range(len(readings)):4    if i < 2:5        result.append(None)⋯
19w ← [12, 9, 15]⋯6else:7    w = readings[i - 2: i + 1]8    result.append(round(sum(w) / 3, 2))⋯values this step[9, 12, 9] → [12, 9, 15]w
20result ← [None, None, 9.0, 10.0, 12.0]⋯7        w = readings[i - 2: i + 1]8        result.append(round(sum(w) / 3, 2))9print('RESULT:', result)values this step[None, None, 9.0, 10.0] → [None, None, 9.0, 10.0, 12.0]result
21i ← 5⋯2result = []3for i in range(len(readings)):4    if i < 2:⋯values this step4 → 5i
22if i < 2:⋯3for i in range(len(readings)):4    if i < 2:5        result.append(None)⋯
23w ← [9, 15, 9]⋯6else:7    w = readings[i - 2: i + 1]8    result.append(round(sum(w) / 3, 2))⋯values this step[12, 9, 15] → [9, 15, 9]w
24result ← [None, None, 9.0, 10.0, 12.0, 11.0]⋯7        w = readings[i - 2: i + 1]8        result.append(round(sum(w) / 3, 2))9print('RESULT:', result)values this step[None, None, 9.0, 10.0, 12.0] → [None, None, 9.0, 10.0, 12.0, 11.0]result
25for i in range(len(readings)):⋯2result = []3for i in range(len(readings)):4    if i < 2:⋯
26stdout ← RESULT: [None, None, 9.0, 10.0, 12.0, 11.0]⋯8        result.append(round(sum(w) / 3, 2))9print('RESULT:', result)values this stepRESULT: [None, None, 9.0, 10.0, 12.0, 11.0]stdout

With pandas

df['x'].rolling(3).mean() computes the mean of each 3-row window in one call. The first two rows have no complete window, so they are NaN and the column is float64. The snapshot shows the raw output; result converts NaN → None and rounds the finite values for comparison with the naive half.

                            library.py
                        

                            import math
import pandas as pd
from dalib.display import set_display
set_display()

readings = [6, 9, 12, 9, 15, 9]
df = pd.DataFrame({'x': readings})
r = df['x'].rolling(3).mean()
result = [round(v, 2) if not math.isnan(v) else None for v in r.tolist()]
print('index:', r.index.tolist())
print('dtype:', r.dtype)
print('values raw:', r.tolist())
print('RESULT:', result)

                        

index: [0, 1, 2, 3, 4, 5]
dtype: float64
values raw: [nan, nan, 9.0, 10.0, 12.0, 11.0]
RESULT: [None, None, 9.0, 10.0, 12.0, 11.0]

Implementation notes

The min_periods parameter controls how many non-NaN values are required to compute a result. rolling(3, min_periods=1) fills the prefix instead of returning NaN.
rolling also supports sum(), min(), max(), std(), and apply(fn) for custom window functions.
The float64 upcast and NaN prefix mirror diff() — use math.isnan or pd.isna when normalising for comparison.
Cross-reference: diff-previous-row (this chapter) for a single-step lag instead of an aggregated window.
Cross-reference: running-total (python-data-basics) for the cumulative-sum approach — accumulating all prior values rather than a fixed-size window.