Mean, Median, Mode: Three Kinds of Average

Say a neighborhood's average income is 100,000 dollars. That could mean: everyone earns 100k, or 9 families earn 50k and one tech founder earns 550k. Same average, wildly different realities. Three different averages solve this ambiguity.

Intuition with a concrete case

import numpy as np
from scipy import stats

salaries = [40_000, 45_000, 50_000, 50_000, 55_000, 
            60_000, 65_000, 70_000, 80_000, 550_000]

print('Mean:', np.mean(salaries))     # 106,500 (misleading)
print('Median:', np.median(salaries))  # 57,500 (typical)
print('Mode:', stats.mode(salaries))   # 50,000 (most common)

When reporters get this wrong

• Average house price: reported as mean, skewed by mansions
• Average response time: mean hides long-tail slow requests
• Average test score: mean hides bimodal distributions (strugglers + high performers)
• Average life expectancy: historical data skewed by infant mortality

Better than one number

When in doubt, report all three plus percentiles. The 25th, 50th (median), 75th, and 95th percentiles together tell a much richer story than any single statistic. A boxplot visualizes this in one picture.

The big idea: average is not one thing. Picking the right statistic is half the battle in honest analysis.