Which statistical measure did Francis Galton use to quantify the strength of the relationship for the line of best fit in his studies of heredity?

• A. The interquartile range
• B. The mode
• C. The mean absolute deviation
• D. The correlation coefficient $r$

Answer: (D)

Verified step by step guidance

1. Understand the context: Francis Galton studied heredity and was interested in quantifying the strength of the relationship between parent and offspring traits.
2. Recall that the line of best fit in such studies represents a linear relationship between two variables, and we need a measure that quantifies how strong this linear relationship is.
3. Review common statistical measures: the interquartile range measures spread, the mode is the most frequent value, and the mean absolute deviation measures average deviation from the mean; none of these directly measure the strength of a linear relationship.
4. Identify that the correlation coefficient is a statistical measure that quantifies the strength and direction of a linear relationship between two variables, ranging from -1 to 1.
5. Conclude that Francis Galton used the correlation coefficient to quantify the strength of the relationship for the line of best fit in his heredity studies.