Edited Anscombe's Quartet Worksheet

Anscombe's quartet comprises four datasets that have nearly identical simple statistical properties, yet appear very different when graphed. Each dataset consists of eleven (x,y) points. They were constructed in 1973 by the statistician Francis Anscombe to demonstrate both the importance of graphing data before analyzing it and the effect of outliers on statistical properties. Use the tools to construct the Least Squares Regression Line for each set. Then compute the following statistics for each dataset: mean of x and y, standard deviation of x and y, correlation between x and y, and the equation of the LSRL. Edited from Anscombe's Quartet by Steve Phelps.

Plot 1

Give the mean of x and y, standard deviation of x and y, correlation between x and y, and the equation of the LSRL.

Plot 2

Give the mean of x and y, standard deviation of x and y, correlation between x and y, and the equation of the LSRL.

Plot 3

Give the mean of x and y, standard deviation of x and y, correlation between x and y, and the equation of the LSRL.

Plot 4

Give the mean of x and y, standard deviation of x and y, correlation between x and y, and the equation of the LSRL.

Conclusions

What do you notice about the means and standard deviations of x and y for the data sets given in each plot?

What do you notice about the correlations and equations of the LSRL for the data sets given in each plot?

What do you notice about the graphs for the data sets given in each plot?

How would you respond to a classmate who says that summary statistics and the equation of the LSRL is enough to describe a bivariate set of data? What suggestions would you give to that person the next time he or she encounters a bivariate set of data?