Weighted Median Calculator
Calculate the weighted median by entering values and their corresponding weights.
Result
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Formula - The weighted median considers the weight of each value. Values are sorted by value, then the cumulative weight is calculated until it exceeds half the total weight.
Batch Import - You can paste multiple values or weights separated by spaces. They will be automatically distributed across the input fields.
When to use weighted median - Use weighted median when different data points have different importance or frequency. Common in statistics, economics, and data analysis.
Weighted Median Formula
To calculate the weighted median manually, follow these steps:
For values [10, 20, 30] with weights [1, 3, 2], total weight is 6. The cumulative weight first exceeds 3 at value 20 (cumulative = 4), so the weighted median is 20.
Sort all values with their weights from smallest to largest. Calculate the cumulative weight as you go through the sorted values. The weighted median is the value where the cumulative weight first reaches or exceeds half of the total weight.
What is Weighted Median?
The weighted median is a measure of central tendency that accounts for the importance (weight) of each value in a dataset.
Unlike the simple median where each value has equal importance, the weighted median assigns different levels of significance to each data point. It's the value where the cumulative weight reaches 50% of the total weight, making it robust against outliers while considering the relative importance of observations.
The weighted median is commonly used in statistics, economics, image processing (for noise reduction), and data analysis. It's particularly valuable when different observations have different levels of reliability or importance, such as survey data weighted by demographics or financial data weighted by transaction volume.
When to Use Weighted Median
The weighted median is essential in many real-world scenarios where data points have varying importance:
- Public Opinion Surveys: Weighting responses by demographic groups ensures representative results.
- Financial Analysis: Weighting data by trading volume or market capitalization gives a more accurate picture.
- Image Processing: Weighted median is used for noise reduction while preserving sharp edges.
Frequently Asked Questions About Weighted Median
- What is the difference between simple and weighted median?
- Simple median treats all values as equally important. Weighted median assigns a weight to each value, so values with higher weights have more influence on determining the central point.
- What are weights used for in weighted median?
- Weights represent the importance, frequency, or reliability of each value. For example, in surveys, you can weight responses by the size of the demographic group they represent.
- When to use weighted median instead of weighted average?
- Use weighted median when your data contains extreme values that could skew the average. Weighted median is more resistant to outliers while respecting the importance of each observation.
- How to interpret weighted median?
- Weighted median is the value where 50% of the total weight lies on each side. It represents the balance point considering both values and their relative importance.
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