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

Frequently Asked Questions

What is standard deviation?

Standard deviation measures the spread or dispersion of data points from the mean. A low SD means data clusters near the mean; a high SD means data is more spread out.

When do I use population vs sample?

Use population SD (divide by N) when you have data for the entire population. Use sample SD (divide by N-1) when your data is a sample from a larger population.

What is variance?

Variance is the average of squared deviations from the mean. Standard deviation is the square root of variance, bringing the units back to the original scale.

Ready to run the numbers?

Open Standard Deviation Calculator (3 values)