Question

peter attempted to use the divide-center method to find the line of best fit on a scatterplot.

what was his mistake?

he had a different number of points to the left of the vertical line than to the right of the vertical line.
he had a different number of points above the line of best fit than below the line of best fit.
he didnt approximate the center of the cluster located on the left side of the vertical line and of the cluster

Explanation:

Understand the divide-center method

The divide-center method is a visual technique used to find a line of best fit on a scatterplot. The process involves:

1. Dividing the data points into two equal halves (left and right) using a vertical line.
2. Finding the "center" (mean or median coordinate) of the cluster of points on the left side, and the "center" of the cluster of points on the right side.
3. Drawing a straight line that passes through both of these center points.

Count the points on each side of the vertical line

Let's count the total number of data points plotted on the graph:

• Points: \((1, 1)\), \((1.5, 5)\), \((3, 8.5)\), \((4.5, 11.5)\), \((5.5, 13.5)\), \((6.5, 20.5)\), \((7, 21.5)\), \((8, 23.5)\), \((9, 24)\), \((10, 30.5)\).
• There are 10 data points in total.
• The vertical dashed line is drawn at \(x = 5\).
• To the left of \(x = 5\), there are 4 points: \((1, 1)\), \((1.5, 5)\), \((3, 8.5)\), \((4.5, 11.5)\).
• To the right of \(x = 5\), there are 6 points: \((5.5, 13.5)\), \((6.5, 20.5)\), \((7, 21.5)\), \((8, 23.5)\), \((9, 24)\), \((10, 30.5)\).

Identify the mistake

Since the divide-center method requires dividing the data set into two halves with an equal number of points on each side of the vertical dividing line, Peter's division is incorrect. He has 4 points on the left and 6 points on the right instead of 5 points on each side.

Match with the given options

Let's evaluate the visible options:

• Option 1: "He had a different number of points to the left of the vertical line than to the right of the vertical line."
• This matches our finding that the points are divided into groups of 4 and 6 instead of equal groups of 5.

Answer:

• (A) He had a different number of points to the left of the vertical line than to the right of the vertical line. (Correct answer)
• (B) He had a different number of points above the line of best fit than below the line of best fit.
• (C) He didn't approximate the center of the cluster located on the left side of the vertical line and of the cluster on the right side.