Weighted Values Standard Deviation Calculator

Calculate weighted standard deviation with a stated population or frequency-weight sample convention.

How to use Weighted Values Standard Deviation Calculator

1. Enter Values and Weights as matching lists where weights are used; separate numbers with commas, spaces, semicolons or new lines. 2. Choose Population or Sample mode. 3. Select Calculate or press Enter, then read weighted standard deviation. 4. Copy result copies the answer; Reset clears the form. Do not use thousands separators inside lists.

Why use this tool?

Describe spread when observations have frequencies or relative weights, while choosing the denominator that matches their meaning.

How the calculation works

Calculate the weighted mean and weighted squared deviations. Population variance divides their sum by total weight. Sample uses whole-number frequency weights and divides by total weight − 1; take the square root for standard deviation. Population accepts non-negative fractional weights. Sample treats weights as repetition counts, requires whole numbers and total frequency from 2 to 9,007,199,254,740,991. Reliability-weight sample estimators are outside scope. Results use up to six decimal places, or six significant digits in scientific notation for nonzero magnitudes below 0.000001. Calculations use browser floating-point arithmetic. Each list supports up to 20,000 numbers. Entry and result magnitudes must not exceed 9,007,199,254,740,991; unrepresentable variance or weighted products are rejected. General descriptive-statistics reference: https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm. Weighted conventions are defined explicitly on this page.

Example

Values = 10,20 and Weights = 1,3 have mean 17.5. Population variance is 18.75, giving standard deviation 4.330127. In frequency-weight Sample mode it is 5.

Practical tip

Choose Population for arbitrary importance weights. Only use Sample when each weight is a whole-number count of repeated observations.