Standard Deviation Calculator (3 values) Formula

Understand the math behind the standard deviation calculator (3 values). Each variable explained with a worked example.

Use the Standard Deviation Calculator (3 values)

Formulas Used

Mean

mean = mean_val

Variance

variance = (pow(x1 - mean_val, 2) + pow(x2 - mean_val, 2) + pow(x3 - mean_val, 2)) / 3

Std Dev

std_dev = sqrt((pow(x1 - mean_val, 2) + pow(x2 - mean_val, 2) + pow(x3 - mean_val, 2)) / 3)

Sample Std

sample_std = sqrt((pow(x1 - mean_val, 2) + pow(x2 - mean_val, 2) + pow(x3 - mean_val, 2)) / 2)

Variables

VariableDescriptionDefault
x1Value 110
x2Value 220
x3Value 330
mean_valDerived value= (x1 + x2 + x3) / 3calculated

How It Works

Standard Deviation

Formula

Population SD = sqrt(sum of (xᵢ - mean)² / N)

Sample SD = sqrt(sum of (xᵢ - mean)² / (N-1))

Steps

1. Calculate the mean (average) 2. Find each value's deviation from the mean 3. Square each deviation 4. Average the squared deviations (divide by N for population, N-1 for sample) 5. Take the square root

Worked Example

Find the standard deviation of 10, 20, 30.

x1 = 10x2 = 20x3 = 30
  1. 01Mean = (10+20+30)/3 = 20
  2. 02Deviations: -10, 0, +10
  3. 03Squared: 100, 0, 100
  4. 04Variance = (100+0+100)/3 ≈ 66.67
  5. 05Std Dev = √66.67 ≈ 8.1650

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Open Standard Deviation Calculator (3 values)