Weighted Values Median Calculator
Find the lower weighted median from matching values and non-negative weights. Values with zero weight are excluded.
How to use Weighted Values Median Calculator
1. Enter Values and Weights as matching lists where weights are used; separate numbers with commas, spaces, semicolons or new lines. 2. Keep all observations on one unit or scoring scale. 3. Select Calculate or press Enter, then read weighted median. 4. Copy result copies the answer; Reset clears the form. Do not use thousands separators inside lists.
Why use this tool?
Describe a central value when observations represent different frequencies or relative weights.
How the calculation works
Sort positive-weight value pairs. Return the first value whose cumulative weight reaches at least half the total. At an exact half-weight boundary this lower weighted-median convention returns the lower value. This is a step-based weighted quantile, not an interpolation or the average of two boundary values. 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/eda351.htm. Weighted conventions are defined explicitly on this page.
Example
Values = 10,20,30 and Weights = 1,1,2 have total weight 4. Cumulative weight first reaches 2 at value 20, so the lower weighted median is 20.
Practical tip
State the convention when comparing results: weighted-median definitions can differ at an exact half-weight boundary.
Frequently asked questions
Why does an equally weighted pair 10,20 return 10?
Half the total weight is reached at 10. This lower weighted-median convention returns that observed value; it does not average 10 and 20.
Are zero-weight observations included?
No. A zero-weight value is excluded before finding the weighted median. At least one weight must be positive.
How should I separate numbers and interpret rounding?
Use commas, spaces, semicolons or new lines between entries. Enter 1000 rather than 1,000: commas separate observations. Repeated values are retained. Displayed results are rounded as stated; keep original readings for later calculations.