Standard Deviation Calculation

1. Enter the "Dataset (multiple data/values)".
   *Enter values ​​separated by commas, spaces, or line breaks.
2. Sample standard deviation, sample variance, population standard deviation, population variance, total, sum, and average are automatically displayed.

It is an index that shows how much data varies around the average value. Deviation indicates the difference from the average value, "how big (small) is it from the average value?" Standard deviation is the "standard deviation" = "the difference from the standard average value."

• The more the data variance (dispersion), the larger the standard deviation
• The less the data variance (dispersion), the larger the standard deviation

• Population standard deviation: Standard deviation calculated for all data sets (entire population)
• Sample standard deviation: Standard deviation calculated for a portion of data sets (samples) selected from the population
• Total: Total number of data
• Variance: Sum of "(data - mean) squared"
• Average: Average of data
• Total: Sum of data

• Standard deviation = sum of "(data - average score) squared" / square root of number of test takers

• Population standard deviation (σ) = √Σ(x - x̄)² / N *√(root) applies to everything
• Population variance (σ²) = Σ(x - x̄)² / N

• σ: population standard deviation
• σ²: population variance
• N: total number
• x: individual value
• x̄: average

• Sample standard deviation (s) = √Σ(x - x̄)² / (N - 1) *√(root) applies to everything
• Sample variance (s²) = Σ(x - x̄)² / (N - 1)

• s: sample standard deviation
• s²: sample variance
• N: total number
• x: individual value
• x̄: average

This tool is available for free.