Briefly |
The median-median line is an alternative to the least-squares regression line. |
The median-median procedure yields a line that fits bivariate data. It's like the least-squares line in the same way that the median is like the mean: it doesn't require a lot of calculation and it's resistant to outliers.
Here's how it works:
1. Divide the data along the horizontal axis into three equal groups. We'll represent them as circles, squares, and triangles. We have created the data here especially to make the calculations easy. |
2. Find the median of the x values and the median of the y-values of each group. These six numbers define three points, one for each group. Let's call them A, B, and C. (The three points are red x's.) |
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3. Draw a line connecting point A to point C. This determines the slope. (Here, the slope is 1 and the line is y = x.) Note that point B is 3 units above the line. |
4. Slide the line one-third of the way towards point B. This determines the intercept and completes our determination of the median-median line, shown in blue. Its equation is at the bottom of the graph. |