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Distribution Shape Guide
- Bell curve (symmetric) → Normal distribution → use mean and std dev
- Right-skewed (long right tail) → Use median, consider log transformation
- Left-skewed (long left tail) → Use median, investigate floor effects
- Bimodal (two peaks) → Two subpopulations mixed, analyze separately
- Uniform (flat) → All values equally likely, check for data issues
- Spike at one value → Check for default/missing value substitution
- Outliers (isolated bars far from main distribution) → Investigate data quality
Examples
Example 1: Basic Histogram from Data
Input data (response times in ms):
120, 145, 132, 118, 156, 143, 127, 139, 151, 128,
135, 142, 119, 148, 133, 126, 141, 155, 130, 137,
122, 149, 136, 125, 144, 131, 158, 140, 124, 147
Generated histogram (10 bins):
100-110ms: ▓ 1
110-120ms: ▓▓▓ 3
120-130ms: ▓▓▓▓▓▓ 6
130-140ms: ▓▓▓▓▓▓▓▓ 8
140-150ms: ▓▓▓▓▓▓▓ 7
150-160ms: ▓▓▓▓ 4
160-170ms: ▓ 1
Shape: Approximately normal (bell curve)
Mean: 136.8ms | Median: 136ms | Std Dev: 11.2ms
Example 2: Descriptive Statistics
Dataset: Product weights (grams) from manufacturing line
n = 500 samples
Statistics:
Mean: 250.3 g
Median: 250.1 g
Mode: 250 g
Std Deviation: 2.4 g
Variance: 5.76
Min: 243.1 g
Max: 257.8 g
Range: 14.7 g
Skewness: 0.12 (slightly right-skewed)
Kurtosis: 2.89 (near normal)
Q1 (25th pct): 248.7 g
Q3 (75th pct): 251.9 g
IQR: 3.2 g
Example 3: Normal Distribution
Dataset: Heights of 1000 adults (cm)
Histogram shape: Bell curve (normal distribution)
140-150cm: ▓▓ 12
150-155cm: ▓▓▓▓▓ 48
155-160cm: ▓▓▓▓▓▓▓▓▓▓▓ 112
160-165cm: ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ 172
165-170cm: ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ 198
170-175cm: ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓ 172
175-180cm: ▓▓▓▓▓▓▓▓▓▓▓ 112
180-185cm: ▓▓▓▓▓ 48
185-195cm: ▓▓ 12
195+cm: ▓ 4
Mean ≈ Median ≈ Mode → Symmetric distribution
Skewness: ~0 (symmetric)