Statistics

Pooled Standard Deviation Calculator

Combine two sample standard deviations into a pooled estimate.

Calculated Output

Pooled SD 4.587

Formula: sp = √(((n₁−1)s₁² + (n₂−1)s₂²) ÷ (n₁+n₂−2))

Step-by-Step Breakdown

1. Values used:

2. Sample 1 size = 12

3. Sample 1 SD = 4

4. Sample 2 size = 15

5. Sample 2 SD = 5

7. Pooled SD = 4.587

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The math behind it

sp = √(((n₁−1)s₁² + (n₂−1)s₂²) ÷ (n₁+n₂−2)). It's used in the two-sample t-test.

n₁ 12 (SD 4), n₂ 15 (SD 5) → pooled SD ≈ 4.58.

Why pool?

It gives a single, more stable variance estimate when groups share a common spread.