W Code - Pattern-Based DSA Learning Platform

Bhanu Bisht

Statistics Fundamentals

Making data-driven decisions with mathematical rigor

Topics

🇮🇳 Indian Context

IT salary analysis, college placement data, and Delhi NCR housing statistics!

Descriptive Statistics

Foundation

Python Implementation

import numpy as np
from scipy import stats

print("=" * 55)
print("DESCRIPTIVE STATISTICS")
print("=" * 55)

# Indian salary data (in lakhs per annum)
salaries = np.array([3.5, 4.2, 5.0, 5.5, 6.0, 6.5, 7.0, 8.0, 12.0, 45.0])

print(f"\n📊 Indian IT Salaries (₹ Lakhs p.a.): {salaries}")

# Central Tendency
print(f"\n--- Central Tendency ---")
print(f"  Mean:   ₹{np.mean(salaries):.1f} Lakhs")
print(f"  Median: ₹{np.median(salaries):.1f} Lakhs")
print(f"  Mode:   N/A (all unique)")
print(f"\n  💡 Mean > Median → Right-skewed (CEO salary pulls mean up!)")

# Spread
print(f"\n--- Spread ---")
print(f"  Range:    {np.ptp(salaries):.1f}")
print(f"  Variance: {np.var(salaries, ddof=1):.2f} (sample)")
print(f"  Std Dev:  {np.std(salaries, ddof=1):.2f}")
Q1, Q3 = np.percentile(salaries, [25, 75])
IQR = Q3 - Q1
print(f"  Q1={Q1:.2f}, Q3={Q3:.2f}, IQR={IQR:.2f}")

# Outlier Detection (IQR Method)
lower_fence = Q1 - 1.5 * IQR
upper_fence = Q3 + 1.5 * IQR
outliers = salaries[(salaries < lower_fence) | (salaries > upper_fence)]
print(f"\n--- Outlier Detection ---")
print(f"  Lower fence: {lower_fence:.2f}")
print(f"  Upper fence: {upper_fence:.2f}")
print(f"  Outliers: {outliers} ← CEO salary!")

# Skewness & Kurtosis
print(f"\n--- Shape ---")
print(f"  Skewness: {stats.skew(salaries):.3f} → Right-skewed")
print(f"  Kurtosis: {stats.kurtosis(salaries):.3f} → Leptokurtic (heavy tail)")

# Feature Scaling
print(f"\n--- ML: Feature Scaling ---")
z_scores = (salaries - np.mean(salaries)) / np.std(salaries)
min_max = (salaries - salaries.min()) / (salaries.max() - salaries.min())
print(f"  Z-score scaled: {np.round(z_scores, 2)}")
print(f"  Min-Max scaled: {np.round(min_max, 2)}")

Key Takeaways

Mean vs Median: use median for skewed data (e.g., salary distributions)

Sample variance uses n-1 (Bessel's correction) for unbiased estimation

IQR method: outlier if x < Q1 - 1.5×IQR or x > Q3 + 1.5×IQR

Right-skewed data → log transform before modeling

Always do EDA first: describe, visualize, detect outliers

import numpy as np from scipy import stats print("=" * 55) print("DESCRIPTIVE STATISTICS") print("=" * 55) # Indian salary data (in lakhs per annum) salaries = np.array([3.5, 4.2, 5.0, 5.5, 6.0, 6.5, 7.0, 8.0, 12.0, 45.0]) print(f"\n📊 Indian IT Salaries (₹ Lakhs p.a.): {salaries}") # Central Tendency print(f"\n--- Central Tendency ---") print(f" Mean: ₹{np.mean(salaries):.1f} Lakhs") print(f" Median: ₹{np.median(salaries):.1f} Lakhs") print(f" Mode: N/A (all unique)") print(f"\n 💡 Mean > Median → Right-skewed (CEO salary pulls mean up!)") # Spread print(f"\n--- Spread ---") print(f" Range: {np.ptp(salaries):.1f}") print(f" Variance: {np.var(salaries, ddof=1):.2f} (sample)") print(f" Std Dev: {np.std(salaries, ddof=1):.2f}") Q1, Q3 = np.percentile(salaries, [25, 75]) IQR = Q3 - Q1 print(f" Q1={Q1:.2f}, Q3={Q3:.2f}, IQR={IQR:.2f}") # Outlier Detection (IQR Method) lower_fence = Q1 - 1.5 * IQR upper_fence = Q3 + 1.5 * IQR outliers = salaries[(salaries < lower_fence) | (salaries > upper_fence)] print(f"\n--- Outlier Detection ---") print(f" Lower fence: {lower_fence:.2f}") print(f" Upper fence: {upper_fence:.2f}") print(f" Outliers: {outliers} ← CEO salary!") # Skewness & Kurtosis print(f"\n--- Shape ---") print(f" Skewness: {stats.skew(salaries):.3f} → Right-skewed") print(f" Kurtosis: {stats.kurtosis(salaries):.3f} → Leptokurtic (heavy tail)") # Feature Scaling print(f"\n--- ML: Feature Scaling ---") z_scores = (salaries - np.mean(salaries)) / np.std(salaries) min_max = (salaries - salaries.min()) / (salaries.max() - salaries.min()) print(f" Z-score scaled: {np.round(z_scores, 2)}") print(f" Min-Max scaled: {np.round(min_max, 2)}")