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).

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