9
QuizMultiple Choice

Drawing Trend Lines — Quiz

Question 9 • Mathematics 8

Serena says that if a regression line is drawn correctly in a scatterplot, there will always be the same number of points above the line as there are below the line. Which of these must be a counterexample to her claim?

Answer
A
a scatterplot with an odd number of points in which the correct regression line passes directly through 0 of the points
B
a scatterplot with an even number of points in which the correct regression line passes directly through 0 of the points
C
a scatterplot with an even number of points in which the correct regression line passes directly through 2 of the points
D
a scatterplot with an odd number of points in which the correct regression line passes directly through 1 of the points

Explanation

If the same number of points are above and below the line, the total number not on the line must be even. In choice A, no points lie on the line, so all the points must be split between above and below; an odd total cannot be split equally. The other choices leave an even number of points to split, so they do not have to contradict Serena’s claim.

AI-written and checked against the verified answer.

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