Final answer:
It seems the question is asking about the median-median line method in statistics to find the line of best fit, but the provided context is not clear. Standard procedures in mathematics do not include 'party lines' with strings and cans or 'progression of achievements through arrows'.
Step-by-step explanation:
The concept of a 'split middle line of progress' or 'party line' mentioned in the question is not a commonly recognized mathematical term. However, it sounds like it might be related to the median-median line method, which is a way to find a line of best fit for a scatter plot in statistics. Despite this, the context provided in the question is insufficient to give a precise answer. Usually, the median-median line method involves dividing the data into three groups, finding the median of each group, and then constructing lines that use the medians to find a slope that represents the general trend of the data.
Please note that the additional references to a 'party line' by tying a third string and can or cup onto the middle of a string and phrase 'progression of achievements through three arrows' do not align with standard mathematical or statistical practices and may be metaphors or concepts from a different subject or context.To find the line of best fit using the median-median approach, you need to first create a chart with two columns. In the first column, list the x-values of the data points, and in the second column, list the corresponding y-values. Then, calculate the median of the x-values and the median of the y-values. Next, find the differences between each x-value and the median x-value, and each y-value and the median y-value. Finally, divide these differences and use the resulting ratio to calculate the slope and y-intercept of the line of best fit.