Symmetric
mean = median = mode
Bell curve / uniform. Perfectly balanced. Use mean to describe center.
MEAN is BEST
Skewed LEFT ◀
mean < median < mode
Tail pulls left → mean gets dragged down. Lower values skew the mean.
TAIL = LOW side
Skewed RIGHT ▶
mean > median > mode
Tail pulls right → mean gets inflated. Higher outliers skew the mean up.
TAIL = HIGH side
Center Choice
skewed → use median
Median is resistant to outliers. Mean is not. Skewed data → always median.
MEDIAN WINS
5-Number Summary
Min, Q₁, Q₂, Q₃, Max
IQR = Q₃ − Q₁. Each section = 25% of data. Outlier if > 1.5×IQR from Q.
IQR = Q₃ − Q₁
Spread Measures
IQR · Standard Dev
IQR for skewed data. Std Dev for symmetric. Both measure spread, not center.
SPREAD ≠ CENTER