📊 Median & Mode Calculator

ODD count (n): Median = value at position (n+1)/2
EVEN count (n): Median = average of values at n/2 and n/2+1

Example (odd): [2, 4, 6, 8, 10] → n=5, pos=3 → Median = 6
Example (even): [2, 4, 6, 8] → n=4, pos=2&3 → Median = (4+6)/2 = 5

No mode: All values appear equally often → [1,2,3,4]
Unimodal: One value is most frequent → [1,2,2,3] → Mode=2
Bimodal: Two values tie for most freq → [1,1,2,2,3] → Mode=1,2
Multimodal: Three or more modes → [1,1,2,2,3,3,4]

Mean: Best for symmetric distributions without outliers
→ Test scores, heights, weights

Median: Best for skewed data or when outliers are present
→ Income, house prices, response times

If Mean > Median → data is right-skewed (outliers high)
If Mean < Median → data is left-skewed (outliers low)
If Mean = Median → data is symmetric

Q1 = Median of the lower half (25th percentile)
Q2 = Median of whole dataset (50th percentile)
Q3 = Median of the upper half (75th percentile)
IQR = Q3 − Q1

Outlier if: x < Q1 − 1.5×IQR
or: x > Q3 + 1.5×IQR

Mean − Mode ≈ 3 × (Mean − Median)

This is Karl Pearson's empirical relation.
It holds approximately for moderately skewed distributions.