Question

An auction house released a list of 25 recently sold paintings. The artist's name and the sale price of each painting appear on the list. Would the correlation coefficient be an appropriate way to summarize the relationship between artist and sale price? Why or why not?

Short answer

No, a correlation coefficient wouldn't be appropriate to summarise the relationship between artist and the sale price because the correlation coefficient is used to measure the degree of a linear relationship between two continuous numerical variables, and 'artist' is a categorical variable.

Step-by-step solution

Understand the nature of the data

Look at the data points provided: artist and sale price. The variable artist is a categorical variable, it identifies to which category each painting belongs to; i.e., who is the artist of the painting. Sale price, on the other hand, is a continuous variable which can take any value within a given range.

Understand the correlation coefficient

The correlation coefficient is a measure that determines the degree to which two variables' movements are associated. It ranges from -1 to 1. A correlation of 1 indicates a perfect positive correlation, while -1 indicates a perfect negative correlation. This is generally used between two continuous/numerical variables.

Determine if a correlation coefficient can be calculated

Given that correlation coefficients are typically used to measure relationships between two numerical or continuous variables, it would not fit to measure the association between a categorical (artist) and a continuous (sale price) variable. Additionally, an artist can't be quantitatively measured which is needed for a correlation coefficient.