A scientist collected data on wing length (in centimeters) and weight (in grams) for a certain type of bird. The data are shown in the scatterplot below.
Which of the following statements best summarizes the relationship between wing length and weight?
(A) Weight tends to decrease as wing length increases.
(B) Weight stays about the same as wing length increases.
(C) Weight tends to increase as wing length increases, but the relationship seems to change for birds with longer wings.
(D) Weight is not related to wing length for heavy birds, but there seems to be a negative relationship for birds with lower weights.
Standards
8.SP.1: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
Correct answer and commentary
Student performance
The correct answer to this question is option C. This question asks students to identify the relationship exhibited in a scatterplot of Weight vs. Wing Length for a certain type of bird. The most striking feature of this plot is that, while heavier birds tend to have longer wings, the relationship is nonlinear. The curve in the scatterplot may be accounted for by the biological processes that drive the growth of this type of bird: perhaps the wings of juvenile birds grow while their bodies grow, but as they mature, their body growth slows while their wings continue to grow. Without more information about this bird and its biology, such statements about the reason for the curve in the plot remain conjecture,but discussions about the processes driving relationships between variables are an important part of interpreting statistical results.
What is clear is that there is an overall relationship between Weight and Wing Length for this type of bird. If the scatterplot were restricted to show only Wing Lengths from 60 cm to 100 cm, option B would be a reasonable choice. As the question is presented, option C correctly describes the relationship: a clear increase in weight as wing length increases with a change in the relationship for birds with longer wings.