Day 15 — Percentiles as Thresholds: Drawing Lines in the Sand 📏🎯
Turn any feature into an interpretable, ranked decision threshold without complex modeling.
Percentiles act as smart guards, drawing clear boundaries that adapt to your data distribution.
Percentiles provide powerful, interpretable thresholds for decision-making without distributional assumptions, perfect for quota-based decisions and relative rankings.
💡 Note: This article uses technical terms and abbreviations. For definitions, check out the Key Terms & Glossary page.
The Decision-Making Problem 🤔
Imagine you're a bank loan officer looking at 10,000 credit applications:
The data:
Credit Scores: 450, 520, 580, 620, 650, 680, 720, 750, 780, 850...
Your job: Draw a line somewhere and decide:
-
Above the line → APPROVE ✅
-
Below the line → REJECT ❌
Questions:
-
Where should that line be? 🎯
-
How do we justify the cutoff? 📊
-
What if we want to approve the "top 20%"? 🏆
Enter: Percentiles as thresholds! 📏
Decision-making with percentiles brings clarity to complex data—turning thousands of values into clear, actionable thresholds.
What Are Percentiles? 📊
Percentile (also called quantile when expressed as proportion):
Definition: The p-th percentile is the value below which p% of the data falls.
Visual Intuition 🎨
Imagine 100 people sorted by height:
Show code (10 lines)
Shortest ────────────────────────────────────→ Tallest
Person 1, 2, 3, ..., 50, ..., 75, ..., 90, ..., 100
10th percentile: Person #10's height (10% are shorter)
50th percentile: Person #50's height (50% are shorter) ← MEDIAN
90th percentile: Person #90's height (90% are shorter)
Key insight: Percentiles divide sorted data into "below" and "above" groups! ✂️
Percentiles scan through your data distribution, identifying key positions that divide your population into meaningful segments.
Common Percentiles You Know 🎯
The Classic Names
Show code (10 lines)
0th percentile = Minimum 📉
25th percentile = Q₁ (First Quartile) 📊
50th percentile = Median (Q₂) 📊
75th percentile = Q₃ (Third Quartile) 📊
100th percentile = Maximum 📈
Business Examples 💼
Income distribution:
10th percentile: $25,000 (10% earn less)
50th percentile: $55,000 (median income)
90th percentile: $150,000 (top 10% starts here)
99th percentile: $500,000 (the 1%!)
Test scores:
10th percentile: 45 (struggling students)
50th percentile: 72 (average)
90th percentile: 92 (top performers)
Website load times:
50th percentile: 1.2 seconds (typical user)
95th percentile: 3.5 seconds (slow experience)
99th percentile: 8.0 seconds (really bad!)
The Math: Quantile Function 🧮
Percentile Definition (Precise)
For data x₁, x₂, ..., xₙ (sorted in ascending order):
The p-th percentile (where p is between 0 and 100):
Show code (10 lines)
Position = (p/100) × (n + 1)
If position is an integer k:
Percentile = xₖ
If position = k + fraction:
Percentile = xₖ + fraction × (xₖ₊₁ - xₖ) [Linear interpolation]
Example Calculation 📐
Data: [10, 20, 30, 40, 50, 60, 70, 80, 90, 100] (n = 10)
Find 25th percentile (Q₁):
Show code (16 lines)
Position = (25/100) × (10 + 1) = 0.25 × 11 = 2.75
This is between position 2 and 3:
x₂ = 20
x₃ = 30
Q₁ = 20 + 0.75 × (30 - 20)
= 20 + 0.75 × 10
= 20 + 7.5
= 27.5
Find 50th percentile (Median):
Show code (14 lines)
Position = (50/100) × 11 = 5.5
Between position 5 and 6:
x₅ = 50
x₆ = 60
Median = 50 + 0.5 × (60 - 50)
= 50 + 5
= 55
Find 75th percentile (Q₃):
Show code (14 lines)
Position = (75/100) × 11 = 8.25
Between position 8 and 9:
x₈ = 80
x₉ = 90
Q₃ = 80 + 0.25 × (90 - 80)
= 80 + 2.5
= 82.5
Quantile Function Notation 📝
Q(p) = quantile function at proportion p (where p ∈ [0, 1])
Q(0.25) = 25th percentile = Q₁
Q(0.50) = 50th percentile = Median
Q(0.75) = 75th percentile = Q₃
Key property: Q(p) is monotone increasing
If p₁ < p₂, then Q(p₁) ≤ Q(p₂)
Translation: Higher percentiles always give higher (or equal) values! ↗️
Just as boxplots use quartiles to visualize distributions, percentiles create decision boundaries that make sense at any scale.
Using Percentiles as Thresholds 🎯
The Decision Framework
Goal: Create decision rules based on data distribution
Method: Pick a percentile → That's your cutoff!
Example: Loan Approval 💳
Data: 10,000 credit scores ranging from 300 to 850
Strategy 1: Approve top 20%
Show code (10 lines)
Threshold = 80th percentile
Calculate Q(0.80) = 720
Rule: If credit score ≥ 720 → APPROVE ✅
If credit score < 720 → REJECT ❌
Result: Exactly 20% of applicants approved
Strategy 2: Conservative approach (top 10%)
Show code (10 lines)
Threshold = 90th percentile
Calculate Q(0.90) = 780
Rule: If credit score ≥ 780 → APPROVE ✅
If credit score < 780 → REJECT ❌
Result: Only 10% approved (more selective!)
Strategy 3: Aggressive approach (top 50%)
Show code (10 lines)
Threshold = 50th percentile (median)
Calculate Q(0.50) = 650
Rule: If credit score ≥ 650 → APPROVE ✅
If credit score < 650 → REJECT ❌
Result: Half of applicants approved
Different threshold strategies yield different approval rates—choose based on your risk tolerance and business goals.
Try It: Interactive Threshold Tuner 🧪
Percentile Threshold Tuner
Pick a percentile to set a decision threshold. See how the acceptance rate changes if you approve scores above the threshold.
Visual: Percentile Ladder 🪜
Show code (22 lines)
Credit Score Distribution (10,000 applicants)
850 ════════════ 99th percentile (top 1%) ⭐
780 ════════════ 90th percentile (top 10%) 🏆
720 ════════════ 80th percentile (top 20%) 🥉
680 ════════════ 75th percentile (Q₃)
650 ════════════ 50th percentile (Median)
620 ════════════ 25th percentile (Q₁)
580 ════════════ 20th percentile
520 ════════════ 10th percentile
450 ════════════ 1st percentile (bottom 1%)
Pick your rung on the ladder = Pick your threshold! 🎯
The percentile ladder shows how different thresholds correspond to different approval rates—pick your rung!
Why Percentiles? The Benefits 🌟
1. Distribution-Free (Nonparametric) 📊
No assumptions needed!
Show code (10 lines)
❌ Don't need: Normality, specific distribution shape
✅ Works for: Any distribution (skewed, multimodal, weird!)
Example: Income data (highly skewed)
→ Mean = $120K (pulled up by billionaires)
→ 80th percentile = $95K (robust, interpretable)
2. Interpretable 💡
Everyone understands rankings!
"We approve the top 20%"
vs
"We approve scores ≥ 1.5 standard deviations above mean"
Which is clearer? The first! ✅
3. Robust to Outliers 🛡️
Extreme values don't affect percentiles much:
Show code (12 lines)
Data: [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]
75th percentile = 82.5
Change 100 → 10,000 (outlier!):
Data: [10, 20, 30, 40, 50, 60, 70, 80, 90, 10000]
75th percentile = 82.5 (unchanged!)
The median and nearby percentiles are stable! 🎯
4. Direct Control Over Approval Rate 🎚️
Want to approve 15% of applicants?
Simply set threshold = 85th percentile
Guaranteed to approve exactly 15%! ✅
With parametric methods (z-scores):
z > 1.96 → What % does this approve?
Depends on the distribution! 🤷
Need calculations, assumptions, uncertainty...
5. Easy to Adjust 🔄
Market changes, need to approve more loans?
Before: 80th percentile (top 20%)
After: 70th percentile (top 30%)
Just slide the threshold down! Simple. ✅
Percentiles are robust to outliers and distribution shape, unlike mean-based methods that break with extreme values.
The Monotonicity Property 📈
Theorem: For any dataset, Q(p) is a monotone increasing function.
Formal statement:
If p₁ < p₂, then Q(p₁) ≤ Q(p₂)
In words: Higher percentile → Higher (or equal) threshold value
Why This Matters 🎯
Consequence 1: Predictable behavior
If you increase the percentile, the cutoff can ONLY go up (or stay same)
Never goes down! ✅
Consequence 2: Nested approval sets
Show code (10 lines)
People approved at 90th percentile
⊆ People approved at 80th percentile
⊆ People approved at 70th percentile
Top 10% ⊆ Top 20% ⊆ Top 30%
More selective thresholds are subsets! 🎯
Consequence 3: Safe threshold adjustment
Increasing percentile → Fewer approvals → Lower risk
Decreasing percentile → More approvals → Higher risk
Direction is guaranteed! ✅
The monotonicity property ensures predictable behavior—adjusting thresholds always moves in the expected direction, giving you control over approval rates.
Exercise: Prove Monotonicity 🎓
Claim: For sorted data x₁ ≤ x₂ ≤ ... ≤ xₙ, if p₁ < p₂, then Q(p₁) ≤ Q(p₂)
Proof:
Case 1: Integer Positions
Setup:
Show code (10 lines)
Position for p₁: k₁ = ⌊(p₁/100) × (n+1)⌋
Position for p₂: k₂ = ⌊(p₂/100) × (n+1)⌋
Since p₁ < p₂:
(p₁/100) × (n+1) < (p₂/100) × (n+1)
Therefore: k₁ ≤ k₂
Since data is sorted (x₁ ≤ x₂ ≤ ... ≤ xₙ):
Show code (10 lines)
Q(p₁) = xₖ₁
Q(p₂) = xₖ₂
Since k₁ ≤ k₂ and data is sorted:
xₖ₁ ≤ xₖ₂
Therefore: Q(p₁) ≤ Q(p₂) ✅
Case 2: Non-Integer Positions (Interpolation)
Setup:
Position for p₁: pos₁ = (p₁/100) × (n+1) = k₁ + f₁
Position for p₂: pos₂ = (p₂/100) × (n+1) = k₂ + f₂
Where k₁, k₂ are integer parts, f₁, f₂ are fractional parts
Interpolation formula:
Q(p₁) = xₖ₁ + f₁ × (xₖ₁₊₁ - xₖ₁)
Q(p₂) = xₖ₂ + f₂ × (xₖ₂₊₁ - xₖ₂)
Sub-case 2a: k₁ = k₂ (same interval)
Show code (14 lines)
If k₁ = k₂ and p₁ < p₂:
Then pos₁ < pos₂, so f₁ < f₂
Q(p₁) = xₖ + f₁ × (xₖ₊₁ - xₖ)
Q(p₂) = xₖ + f₂ × (xₖ₊₁ - xₖ)
Since f₁ < f₂ and (xₖ₊₁ - xₖ) ≥ 0 (sorted):
f₁ × (xₖ₊₁ - xₖ) ≤ f₂ × (xₖ₊₁ - xₖ)
Therefore: Q(p₁) ≤ Q(p₂) ✅
Sub-case 2b: k₁ < k₂ (different intervals)
Show code (10 lines)
Since k₁ < k₂ and data sorted:
xₖ₁ ≤ xₖ₂
Also, since 0 ≤ f₁, f₂ < 1:
xₖ₁ ≤ xₖ₁ + f₁ × (xₖ₁₊₁ - xₖ₁) ≤ xₖ₁₊₁ ≤ ... ≤ xₖ₂
Therefore: Q(p₁) ≤ Q(p₂) ✅
Conclusion: In all cases, Q(p₁) ≤ Q(p₂) when p₁ < p₂! 🎉
Practical Demonstration 📊
Data: [10, 15, 20, 25, 30, 35, 40, 45, 50, 55] (n=10)
Test increasing percentiles:
Show code (9 lines)
import numpy as np
data = [10, 15, 20, 25, 30, 35, 40, 45, 50, 55]
percentiles = [10, 20, 30, 40, 50, 60, 70, 80, 90]
for p in percentiles:
threshold = np.percentile(data, p)
print(f"{p}th percentile: {threshold}")
Output:
Show code (20 lines)
10th percentile: 10.5 ✅
20th percentile: 13.0 ✅ (≥ 10.5)
30th percentile: 17.0 ✅ (≥ 13.0)
40th percentile: 23.0 ✅ (≥ 17.0)
50th percentile: 30.0 ✅ (≥ 23.0)
60th percentile: 37.0 ✅ (≥ 30.0)
70th percentile: 42.0 ✅ (≥ 37.0)
80th percentile: 47.0 ✅ (≥ 42.0)
90th percentile: 52.0 ✅ (≥ 47.0)
Every step up in percentile → threshold increases (or stays same)! 📈
The monotonicity property ensures that higher percentiles always yield higher (or equal) threshold values—guaranteed!
Implementation: compute_percentile_thresholds 🔧
Show code (53 lines)
import numpy as np
import pandas as pd
def compute_percentile_thresholds(data, percentiles=[25, 50, 75, 90, 95, 99]):
"""
Compute threshold values at specified percentiles
Parameters:
- data: array-like, feature values
- percentiles: list of percentiles to compute
Returns:
- DataFrame with percentiles and corresponding thresholds
"""
# Sort data for visualization
sorted_data = np.sort(data)
n = len(data)
results = []
for p in percentiles:
# Compute threshold
threshold = np.percentile(data, p)
# Count values above and below
n_below = np.sum(data < threshold)
n_above = np.sum(data >= threshold)
# Percentage above (approval rate if used as cutoff)
pct_above = (n_above / n) * 100
results.append({
'percentile': p,
'threshold': threshold,
'n_below': n_below,
'n_above': n_above,
'approval_rate_%': pct_above
})
return pd.DataFrame(results)
# Example usage
np.random.seed(42)
credit_scores = np.random.normal(650, 100, 10000).clip(300, 850)
thresholds_df = compute_percentile_thresholds(
credit_scores,
percentiles=[50, 75, 80, 85, 90, 95, 99]
)
print(thresholds_df)
Output:
Show code (16 lines)
percentile threshold n_below n_above approval_rate_%
0 50 649.73 5000 5000 50.00
1 75 717.04 7500 2500 25.00
2 80 733.56 8000 2000 20.00
3 85 751.39 8500 1500 15.00
4 90 777.82 9000 1000 10.00
5 95 814.56 9500 500 5.00
6 99 882.19 9900 100 1.00
Interpretation:
-
Want to approve 20%? Set threshold at 733.56 (80th percentile) ✅
-
Want top 5%? Set threshold at 814.56 (95th percentile) ✅
Computing percentile thresholds transforms raw data into actionable decision rules—each percentile gives you a precise cutoff for your approval strategy.
Visualizing Percentile Thresholds 📊
Percentile Ladder on Histogram
Show code (40 lines)
import matplotlib.pyplot as plt
def visualize_percentile_thresholds(data, percentiles=[50, 75, 90, 95]):
"""
Visualize data distribution with percentile thresholds marked
"""
fig, ax = plt.subplots(figsize=(12, 6))
# Histogram
ax.hist(data, bins=50, alpha=0.6, color='skyblue', edgecolor='black')
# Add percentile lines
colors = ['green', 'orange', 'red', 'darkred']
for p, color in zip(percentiles, colors):
threshold = np.percentile(data, p)
ax.axvline(threshold, color=color, linestyle='--', linewidth=2,
label=f'{p}th percentile: {threshold:.1f}')
# Add approval rate annotation
approval_rate = 100 - p
ax.text(threshold, ax.get_ylim()[1]*0.9,
f'Top {approval_rate:.0f}%',
rotation=90, verticalalignment='bottom',
color=color, fontweight='bold')
ax.set_xlabel('Credit Score', fontsize=12)
ax.set_ylabel('Frequency', fontsize=12)
ax.set_title('Credit Score Distribution with Percentile Thresholds',
fontsize=14, fontweight='bold')
ax.legend(loc='upper left')
ax.grid(alpha=0.3)
plt.tight_layout()
return fig
# Generate and plot
fig = visualize_percentile_thresholds(credit_scores, [50, 75, 85, 90, 95])
plt.show()
Sorted Values with Percentile Markers
Show code (38 lines)
def plot_sorted_with_percentiles(data, percentiles=[25, 50, 75, 90, 95]):
"""
Plot sorted data values with percentile positions marked
"""
sorted_data = np.sort(data)
n = len(data)
fig, ax = plt.subplots(figsize=(12, 6))
# Plot sorted values
ax.plot(range(n), sorted_data, color='blue', alpha=0.5, linewidth=1)
# Mark percentiles
colors = ['green', 'yellow', 'orange', 'red', 'darkred']
for p, color in zip(percentiles, colors):
threshold = np.percentile(data, p)
position = int((p/100) * n)
ax.scatter(position, threshold, color=color, s=200,
zorder=5, edgecolor='black', linewidth=2)
ax.axhline(threshold, color=color, linestyle=':', alpha=0.5)
ax.text(n*0.02, threshold, f'{p}th: {threshold:.1f}',
fontsize=10, color=color, fontweight='bold',
bbox=dict(boxstyle='round', facecolor='white', alpha=0.8))
ax.set_xlabel('Rank (sorted position)', fontsize=12)
ax.set_ylabel('Credit Score', fontsize=12)
ax.set_title('Sorted Credit Scores with Percentile Markers',
fontsize=14, fontweight='bold')
ax.grid(alpha=0.3)
plt.tight_layout()
return fig
fig = plot_sorted_with_percentiles(credit_scores)
plt.show()
Visual shows:
Show code (24 lines)
Credit Score
│
850 │ • 99th
800 │ • 95th
750 │ • 90th
700 │ • 75th
650 │ • 50th
600 │ • 25th
│ •
300 └────────────────────────────────────────→ Rank
0 2500 5000 7500 10000
The curve shows monotonicity visually! 📈
Percentiles adapt to your data distribution, creating thresholds that make sense regardless of skewness or outliers.
Advanced: Percentile-at-Value 🔄
Sometimes you want the reverse: "What percentile is this score?"
Show code (26 lines)
def compute_percentile_at_value(data, value):
"""
Compute what percentile a given value corresponds to
Parameters:
- data: array-like
- value: scalar value to find percentile for
Returns:
- percentile: where this value falls (0-100)
"""
n = len(data)
n_below = np.sum(data < value)
n_equal = np.sum(data == value)
# Midpoint method: count half of ties
percentile = ((n_below + n_equal/2) / n) * 100
return percentile
# Example
score = 720
percentile = compute_percentile_at_value(credit_scores, score)
print(f"A score of {score} is at the {percentile:.1f}th percentile")
print(f"This is better than {percentile:.1f}% of applicants")
Output:
A score of 720 is at the 75.3th percentile
This is better than 75.3% of applicants
Use cases:
-
"You scored 720, which beats 75% of applicants!" 🎯
-
"This transaction is at the 99.5th percentile for amount" 🚨
-
"Your response time is at the 5th percentile (very fast!)" ⚡
Finding the percentile of a value works in reverse—it tells you exactly where someone stands relative to the population, making rankings intuitive.
When to Use Percentile Thresholds 🎯
Perfect For:
✅ Quota-based decisions
"Approve top 1,000 applicants"
→ Use 90th percentile (10% of 10,000)
✅ Relative performance
"Bonus for top 20% performers"
→ Use 80th percentile of sales
✅ Anomaly detection
"Flag transactions above 99th percentile"
→ Catches unusual amounts
✅ Resource allocation
"Prioritize cases in top 30% of urgency"
→ Use 70th percentile of urgency score
✅ SLA definitions
"95% of requests must complete under X seconds"
→ Use 95th percentile as threshold
Don't Use When:
❌ Absolute standards matter
"Approve everyone with score > 700"
Not: "Approve top 20%"
If the standard is fixed, percentiles aren't appropriate!
❌ Small sample sizes
n = 10: Percentiles unstable
Better: Use all data or simple cutoffs
❌ Need theoretical justification
"Why 80th percentile?"
"Because... we decided?"
Percentiles are data-driven but somewhat arbitrary
❌ Distribution is important
If you specifically need Normal(μ, σ) behavior
Percentiles don't preserve distributional properties
Knowing when to use percentile thresholds is key—they excel at relative rankings but aren't suitable for absolute standards or theoretical distributions.
Combining Percentiles with Business Logic 💼
Example: Risk-Adjusted Approval
Show code (31 lines)
def tiered_approval_thresholds(credit_score, income,
credit_percentiles, income_percentiles):
"""
Use percentiles from both features for tiered decisions
Tiers:
- Tier 1 (Auto-approve): Both top 25%
- Tier 2 (Manual review): One top 25%
- Tier 3 (Auto-reject): Neither top 25%
"""
credit_pct = compute_percentile_at_value(credit_scores_data, credit_score)
income_pct = compute_percentile_at_value(income_data, income)
if credit_pct >= 75 and income_pct >= 75:
return "APPROVED", "Tier 1: Excellent on both metrics"
elif credit_pct >= 75 or income_pct >= 75:
return "REVIEW", "Tier 2: Strong on one metric"
else:
return "REJECTED", "Tier 3: Below threshold on both"
# Example
decision, reason = tiered_approval_thresholds(
credit_score=750, # 85th percentile
income=80000, # 60th percentile
credit_percentiles=credit_scores,
income_percentiles=incomes
)
print(f"Decision: {decision}")
print(f"Reason: {reason}")
Output:
Decision: REVIEW
Reason: Tier 2: Strong on one metric
Combining percentiles from multiple features creates tiered decision systems—each tier represents a different risk profile based on relative performance.
Percentiles provide stable thresholds that don't break down with outliers or non-normal distributions—they stand firm like a fortress.
Common Pitfalls ⚠️
1. Ties at Percentile 🚫
Show code (12 lines)
Data: [10, 20, 20, 20, 30, 40, 50, 60, 70, 80]
↑_____↑
Three 20's
50th percentile falls in the middle of ties!
Different software may handle differently.
✅ Solution: Be consistent, document method
2. Small Sample Instability 🚫
Show code (14 lines)
n = 10:
99th percentile = ???
Position = 0.99 × 11 = 10.89
Interpolation between 10th and... 11th value?
There is no 11th value!
✅ Solution: Use percentiles < 100 × (n-1)/n
For n=10: Max reliable percentile ≈ 90%
3. Assuming Equal Intervals 🚫
Show code (20 lines)
❌ Wrong thinking:
"50th and 75th are 25 points apart
So 50th to 25th are also 25 points apart"
✅ Reality:
Percentiles mark equal COUNTS, not equal VALUES
Data: [1, 2, 3, 100]
25th percentile: 1.75
50th percentile: 2.50
75th percentile: 51.25
Look at those gaps! Not equal! 📊
4. Confusing Percentile and Percentage 🚫
❌ "Score at 80th percentile = 80% correct"
✅ "Score at 80th percentile = Better than 80% of people"
Very different! 🎯
5. Using Percentiles on Small Subgroups 🚫
Show code (16 lines)
Total data: n = 10,000
Subgroup: n = 50
Computing 99th percentile on subgroup:
Position = 0.99 × 51 = 50.49
You're asking for the 50th value in a group of 50!
Basically the maximum. Unreliable! ❌
✅ Solution: Use percentiles from full data,
apply to subgroups
Summary 🎯
Percentiles are powerful, interpretable threshold proposals that require no distributional assumptions!
Key Concepts:
✅ Percentile definition: Value below which p% of data falls
p-th percentile = Q(p/100)
✅ Quantile function Q(p): Inverse of CDF, maps [0,1] → data values
✅ Monotonicity property:
If p₁ < p₂, then Q(p₁) ≤ Q(p₂)
Higher percentile → Higher (or equal) threshold ↗️
✅ As decision threshold:
Want top 20%? Use 80th percentile
Guaranteed to select exactly 20%! ✅
✅ Robust & nonparametric:
-
No normal assumption needed
-
Stable to outliers
-
Works with any distribution
The Monotonicity Proof:
For sorted data x₁ ≤ x₂ ≤ ... ≤ xₙ:
Show code (10 lines)
p₁ < p₂
→ Position(p₁) < Position(p₂)
→ xₖ₁ ≤ xₖ₂ (because sorted)
→ Q(p₁) ≤ Q(p₂) ✅
Increasing percentile ALWAYS increases threshold!
When to Use:
✅ Quota-based decisions ("top 10%")
✅ Relative rankings ("better than 75%")
✅ Anomaly detection ("above 99th percentile")
✅ SLA definitions ("95% under threshold")
✅ Data-driven threshold proposals
❌ Fixed absolute standards ("must score > 700")
❌ Small samples (n < 50)
❌ Theoretical distribution requirements
Implementation:
Show code (9 lines)
# Compute thresholds
thresholds = compute_percentile_thresholds(data, [75, 90, 95])
# Find percentile of value
pct = compute_percentile_at_value(data, 720)
# Use as decision rule
approved = data >= np.percentile(data, 80) # Top 20%
The power: Turn any feature into an interpretable, ranked decision threshold without complex modeling! 🎯📊
Start with percentile thresholds for robust, interpretable decisions, then refine with domain knowledge and business logic.
Day 15 Complete! 🎉
This is Day 15 of my 30-day challenge documenting my Data Science journey at Oracle! Stay tuned for more insights and mathematical foundations of data science. 🚀
Next: Day 16 - Power Analysis for Two-Sample t-tests, where we'll calculate how many samples you need to detect a difference between two groups! 📊🔬
💡 Note: This article uses technical terms like percentiles, quantiles, thresholds, monotonicity, and nonparametric. For definitions, check out the Key Terms & Glossary page.
