Question

the graph below represents winning times for the womens 400 - meter freestyle swim for the olympics. what two points on the graph should you pick to help determine the line of best fit? points (year, time)

Explanation:

Step1: Recall line - fitting concept

To find the best - fitting line, we usually look for points that represent the general trend of the data. We want to avoid outliers (points that are far from the general pattern).

Step2: Analyze the data points

Looking at the given data points (year, time) pairs, we should choose points that seem to follow the overall decrease in winning times over the years. Points that are too high or too low compared to the neighboring points might be outliers. For example, if most of the times are decreasing steadily and there is a point with a much higher time than its neighbors, it could be an outlier. A good choice would be points that are in the middle of the data distribution in terms of both the year and the time values. Let's assume we have a scatter - plot of these points. We might choose two points that seem to lie on a line that passes through the "center" of the cloud of points. For simplicity, if we consider the earliest and a middle - of - the - range point. Let's say we choose (24, 6.02) and (56, 4.54) as they seem to represent the general downward trend of winning times as the years progress.

Answer:

(24, 6.02), (56, 4.54)