Standard Deviation Calculator

Calculate the standard deviation of your dataset. Understand the formula and its use below.

Formula and Uses

Standard Deviation

Formula: σ = √[ Σ ( xi - μ )² / N ]

Where:
σ = Standard deviation
Σ = Sum of all values
xi = Each value in the dataset
μ = Mean of the dataset
N = Number of values in the dataset

Uses: Standard deviation measures the amount of variation or dispersion in a dataset. A low standard deviation means the data points are close to the mean, while a high standard deviation indicates that the data points are spread out.

Calculation Process

Step-by-Step Calculation

Input Data: Enter your dataset as comma-separated values. For example: 10, 20, 30, 40, 50.
Calculate the Mean (μ):
Add all the values together and divide by the number of values (N).
```
μ = (x1 + x2 + ... + xN) / N
```
Calculate Each Deviation from the Mean:
For each value in your dataset, subtract the mean and square the result.
```
(xi - μ)²
```
Sum of Squared Deviations:
Add all the squared deviations together.
```
Σ (xi - μ)²
```
Calculate Variance:
Divide the sum of squared deviations by the number of values (N).
```
Variance = Σ (xi - μ)² / N
```
Calculate Standard Deviation (σ):
Take the square root of the variance to get the standard deviation.
```
σ = √Variance
```

Example: If you have data points 10, 20, 30, 40, and 50:

Mean (μ) = (10 + 20 + 30 + 40 + 50) / 5 = 30
Squared deviations: (10 - 30)² = 400, (20 - 30)² = 100, (30 - 30)² = 0, (40 - 30)² = 100, (50 - 30)² = 400
Sum of squared deviations = 400 + 100 + 0 + 100 + 400 = 1000
Variance = 1000 / 5 = 200
Standard Deviation (σ) = √200 ≈ 14.14