Number Line (0 to 100)
The shaded blue region represents ±1 Standard Deviation from the Mean. The colored lines show individual deviations.
Sample Standard Deviation Formula
s = √ (
Σ (xi - x̄)²
n - 1
)
Step 1: Calculate the Mean (x̄)
Sum all values and divide by the sample size (n = 5).
x̄ = (20 + 35 + 50 + 65 + 80) / 5 = 50.00
Step 2: Calculate Deviations
Find how far each point is from the mean, then square it to make it positive.
| Point | Value (x) | Dev (x - x̄) | Sq Dev (x - x̄)² |
|---|
Step 3: Sum of Squares (SS)
Add up all the squared deviations from the table.
SS = Σ (x - x̄)²
SS = 900 + 225 + 0 + 225 + 900
SS = 900 + 225 + 0 + 225 + 900
SS = 2250.00
Step 4: Sample Variance (s²)
Divide the Sum of Squares by n - 1 (Bessel's correction). Here, 5 - 1 = 4.
s² = 2250.00 / 4 = 562.50
Step 5: Sample Std. Dev. (s)
Take the square root of the variance to return to the original units.
s = √562.50 = 23.72