IQR Outlier Flags - Data Cleaning Step by Step

Flag values that lie outside Tukey's 1.5×IQR fences. Compute Q1 and Q3 (the 25th and 75th percentiles), set fences at Q1 − 1.5×IQR and Q3 + 1.5×IQR, then mark any value strictly outside those fences as an outlier. By hand, sort the list and pick the quartile positions directly. With pandas, use Series.quantile() to get the same values in one call.

By hand

Sort the values, then compute Q1 and Q3 by picking the positions at (n−1)×0.25 and (n−1)×0.75 in the sorted array. With n=9 values, these positions are (8)×0.25 = 2 and (8)×0.75 = 6 — exact integers, so no interpolation is needed. The naive half picks sv[2] and sv[6] directly using int((n-1)*0.25), which matches pandas' default linear-interpolation quantile exactly for this data. Fences: lo = Q1 − 1.5×IQR, hi = Q3 + 1.5×IQR. Flag any value where v < lo or v > hi.

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

                            values = [4, -10, 8, 50, 6, 12, 10, 16, 14]
sv = sorted(values)
n = len(sv)
q1 = sv[int((n - 1) * 0.25)]
q3 = sv[int((n - 1) * 0.75)]
iqr = q3 - q1
lo = q1 - 1.5 * iqr
hi = q3 + 1.5 * iqr
result = []
for v in values:
    result.append(v < lo or v > hi)
print('RESULT:', result)

                        
1values ← [4, -10, 8, 50, 6, 12, 10, 16, 14]1values = [4, -10, 8, 50, 6, 12, 10, 16, 14]2sv = sorted(values)⋯values this step[4, -10, 8, 50, 6, 12, 10, 16, 14]values
2sv ← [-10, 4, 6, 8, 10, 12, 14, 16, 50]1values = [4, -10, 8, 50, 6, 12, 10, 16, 14]2sv = sorted(values)3n = len(sv)⋯values this step[-10, 4, 6, 8, 10, 12, 14, 16, 50]sv
3n ← 9⋯2sv = sorted(values)3n = len(sv)4q1 = sv[int((n - 1) * 0.25)]⋯values this step9n
4q1 ← 6⋯3n = len(sv)4q1 = sv[int((n - 1) * 0.25)]5q3 = sv[int((n - 1) * 0.75)]⋯values this step6q1
5q3 ← 14⋯4q1 = sv[int((n - 1) * 0.25)]5q3 = sv[int((n - 1) * 0.75)]6iqr = q3 - q1⋯values this step14q3
6iqr ← 8⋯5q3 = sv[int((n - 1) * 0.75)]6iqr = q3 - q17lo = q1 - 1.5 * iqr⋯values this step8iqr
7lo ← -6.0⋯6iqr = q3 - q17lo = q1 - 1.5 * iqr8hi = q3 + 1.5 * iqr⋯values this step-6.0lo
8hi ← 26.0⋯7lo = q1 - 1.5 * iqr8hi = q3 + 1.5 * iqr9result = []⋯values this step26.0hi
9result ← []⋯8hi = q3 + 1.5 * iqr9result = []10for v in values:⋯values this step[]result
10v ← 4⋯9result = []10for v in values:11    result.append(v < lo or v > hi)⋯values this step4v
11result ← [False]⋯10for v in values:11    result.append(v < lo or v > hi)12print('RESULT:', result)values this step[] → [False]result
12v ← -10⋯9result = []10for v in values:11    result.append(v < lo or v > hi)⋯values this step4 → -10v
13result ← [False, True]⋯10for v in values:11    result.append(v < lo or v > hi)12print('RESULT:', result)values this step[False] → [False, True]result
14v ← 8⋯9result = []10for v in values:11    result.append(v < lo or v > hi)⋯values this step-10 → 8v
15result ← [False, True, False]⋯10for v in values:11    result.append(v < lo or v > hi)12print('RESULT:', result)values this step[False, True] → [False, True, False]result
16v ← 50⋯9result = []10for v in values:11    result.append(v < lo or v > hi)⋯values this step8 → 50v
17result ← [False, True, False, True]⋯10for v in values:11    result.append(v < lo or v > hi)12print('RESULT:', result)values this step[False, True, False] → [False, True, False, True]result
18v ← 6⋯9result = []10for v in values:11    result.append(v < lo or v > hi)⋯values this step50 → 6v
19result ← [False, True, False, True, False]⋯10for v in values:11    result.append(v < lo or v > hi)12print('RESULT:', result)values this step[False, True, False, True] → [False, True, False, True, False]result
20v ← 12⋯9result = []10for v in values:11    result.append(v < lo or v > hi)⋯values this step6 → 12v
21result ← [False, True, False, True, False, False]⋯10for v in values:11    result.append(v < lo or v > hi)12print('RESULT:', result)values this step[False, True, False, True, False] → [False, True, False, True, False, False]result
22v ← 10⋯9result = []10for v in values:11    result.append(v < lo or v > hi)⋯values this step12 → 10v
23result ← [False, True, False, True, False, False, False]⋯10for v in values:11    result.append(v < lo or v > hi)12print('RESULT:', result)values this step[False, True, False, True, False, False] → [False, True, False, True, False, False, False]result
24v ← 16⋯9result = []10for v in values:11    result.append(v < lo or v > hi)⋯values this step10 → 16v
25result ← [False, True, False, True, False, False, False, False]⋯10for v in values:11    result.append(v < lo or v > hi)12print('RESULT:', result)values this step[False, True, False, True, False, False, False] → [False, True, False, True, False, False, False, False]result
26v ← 14⋯9result = []10for v in values:11    result.append(v < lo or v > hi)⋯values this step16 → 14v
27result ← [False, True, False, True, False, False, False, False, False]⋯10for v in values:11    result.append(v < lo or v > hi)12print('RESULT:', result)values this step[False, True, False, True, False, False, False, False] → [False, True, False, True, False, False, False, False, False]result
28for v in values:⋯9result = []10for v in values:11    result.append(v < lo or v > hi)⋯
29stdout ← RESULT: [False, True, False, True, False, False, False, False, False]⋯11    result.append(v < lo or v > hi)12print('RESULT:', result)values this stepRESULT: [False, True, False, True, False, False, False, False, False]stdout

With pandas

Series.quantile(p) uses linear interpolation by default. For this data the 25th and 75th percentile positions land on exact indices, so the result equals the naive pick. Build the fence flags with (df['x'] < lo) | (df['x'] > hi).

                            library.py
                        

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

values = [4, -10, 8, 50, 6, 12, 10, 16, 14]
df = pd.DataFrame({'x': values})
q1 = df['x'].quantile(0.25)
q3 = df['x'].quantile(0.75)
iqr = q3 - q1
lo = q1 - 1.5 * iqr
hi = q3 + 1.5 * iqr
flags = (df['x'] < lo) | (df['x'] > hi)
result = flags.tolist()
print('q1:', q1, 'q3:', q3, 'iqr:', iqr)
print('lo:', lo, 'hi:', hi)
print('values:', df['x'].tolist())
print('RESULT:', result)

                        

q1: 6.0 q3: 14.0 iqr: 8.0
lo: -6.0 hi: 26.0
values: [4, -10, 8, 50, 6, 12, 10, 16, 14]
RESULT: [False, True, False, True, False, False, False, False, False]

Implementation notes

The quartile method matters for parity: int((n-1)*p) gives the exact position only when (n-1)*p is an integer. Choosing n=9 makes both Q1 and Q3 positions integers, so naive and pandas agree without approximation.
Values exactly on a fence are not flagged — the condition is strict (< and >), consistent with Tukey's original definition.
The 1.5×IQR multiplier is Tukey's standard threshold; use 3×IQR for "extreme" outlier fences.
Cross-reference: stats-percentiles (statistics chapter) for a deeper look at percentile methods and interpolation.