# Median-Median Method

## Median-Median Method

Graphic linear regression process that makes it possible to find the parameters of a line of regression by using the median of the data in a distribution.

The median-median method is most often used when the distribution has a large quantity of data and is particularly effective when this distribution includes inconsistent data. This method has several steps:

• Arranging the points so that the x values are in ascending order (if two x values are identical, they are ordered based on the y value);
• Separating the points on the scatter plot into three groups of equal frequencies (so that the difference between the number of data in each group is minimal);
• For each group, determining the median of the x coordinates and the median of the y coordinates M1 (x, y), M2 (x, y) and M3 (x, y);
• Determining the mean of the x coordinates and the mean of the y coordinates of the three median points: P1 ($$\overline{x}, \overline{y}$$
• Positioning the coordinate points M1 (x, y) and M3 (x, y) and drawing a line through them;
• The line of regression is parallel to the line that passes through the points M1 (x, y) and M3 (x, y);
• The line of regression passes through the point P1 ($$\overline{x}, \overline{y}$$);
• The y-intercept P2 (0, y) of the line of regression is calculated using the point P1($$\overline{x}, \overline{y}$$) and the slope of the line that passes through M1(x, y) and M3 (x, y).