The Median-Median Line. Lesson 3.4. Have you noticed that you and your classmates frequently find different equations to model the same data?. The median-median line is one of the simplest methods.
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The Median-Median Line
Have you noticed that you and your classmates frequently find different equations to model the same data?
The median-median line is one of the simplest methods.
The procedure for finding the median-median line uses three points M1, M2, and M3 to represent the entire data set, and the equation that best fits these three points is taken as the line of fit for the entire set of data.
To find the three points that will represent the entire data set, you first order all the data points by their domain value (the x-value) and then divide the data into three
If the number of points is not divisible by 3, then you split them so that the first and last groups are the same size. For example:
18 data points: split into groups of 6-6-6
19 data points: split into groups of 6-7-6
20 data points: split into groups of 7-6-7
You then order the y-values within each of the groups. The representative point for each group has the coordinates of the median x-value of that group and the median y-value of that group.
Because a good line of fit divides the data evenly, the median-median line should pass between M1, M2, and M3, but be closer to M1 and M3 because they represent two-thirds of the data.
To accomplish this, you can find the y-intercept of the line through M1 and M3, and the y-intercept of the line through M2 that has the same slope.
The mean of the three y-intercepts of the lines through M1, M2, and M3 gives you the y-intercept of a line that satisfies these requirements.
On your graph, mark the three representative points used in the median-median process. Add the line to this graph.
Answer these questions about your data and model.
a. Use your median-median line to interpolate two points for which you did not collect data. What is the real-world meaning of each of these points?
b. Which two points differ the most from the value predicted by your equation? Explain why.
c. What is the real-world meaning of your slope?
d. Find the y-intercept of your median-median line. What is its real-world meaning?
e. What are the domain and range for your data? Why?
f. Compare the median-median line method to the method you used in Lesson 3.3 to find the line of fit. What are the advantages and disadvantages of each? In your opinion, which method produces a better line of fit? Why?