How to Calculate Standard Deviation

Understanding Standard Deviation

Standard deviation measures the spread or dispersion of a dataset relative to its mean. A low standard deviation indicates that data points are close to the mean, while a high standard deviation suggests a broader spread.

Formula

For a population standard deviation:

σ = √(Σ (xᵢ – μ)² / N)

Where μ is the mean and N is the total number of data points.

Example

If you have the data points [10, 20, 30, 40, 50]:

• Mean (μ) = (10 + 20 + 30 + 40 + 50) / 5 = 30
• Variance = average of (xᵢ – μ)²
• Standard Deviation = √(Variance)

Try It Yourself

Enter Data Values (comma-separated): Calculate Standard Deviation

FAQ

1. How do I interpret a high standard deviation?

A higher standard deviation means your data points are more spread out. This could indicate variability or inconsistencies in your dataset.

2. Do I need a large sample size for accurate results?

Generally, a larger sample size gives a more accurate picture. For small samples, consider the sample standard deviation formula (n-1 in the denominator).

3. Which other calculator might help analyze data?

You can also look at our Average Calculator to find the mean of your data quickly.