Question

which statement best describes whether the line shown on the graph below is the best fit to the data?
the line
is not
the best fit because
(select)
(select)
the line passes close to the first three points
approximately half the data points lie on either side of the line
the line does not go through all the points of the data set
it does not go through any of the data points

Explanation:

Step1: Understand the concept of best - fit line

A best - fit line (or trend line) for a scatter plot should have approximately half of the data points on either side of the line. This helps to balance the overall distribution of the data points around the line.

Step2: Analyze each option

• Option 1: "the line passes close to the first three points" is not a valid criterion for a best - fit line. A best - fit line should consider all the data points, not just the first few.
• Option 2: "approximately half the data points lie on either side of the line" is the correct criterion for a best - fit line.
• Option 3: "the line does not go through all the points of the data set": A best - fit line is not required to pass through all the data points. In fact, for a scatter plot with multiple points, it is very rare for a line to pass through all of them.
• Option 4: "it does not go through any of the data points": Similar to the previous option, not passing through any data points is not a reason for a line not being a best - fit line.

Answer:

approximately half the data points lie on either side of the line