Rather than asking about the predictive power of a dataset, I think it's intuitive to ask about the predictive power of a model. My reasoning is as follows;

A dataset can be univariate, bivariate or multivariate types. The dataset can contain only numerical features or categorical features or both. Suppose there is a univariate dataset with a negative skewed distribution. In such a case the mean, median will be less than the mode. Now suppose this univariate dataset consist of continuous data type. Knowing that its distribution is negatively skewed has already given the analyst a clue about its symmetry or distribution. So basis of this brief introduction, as an analyst will I be interested to know the predictive power of a dataset or the model('s) that I build using this dataset, is a question worth discussing?

There have been several studies in literature that have discussed the model's predictive power like 1,2,3 (see references). In contrast, I have not come across any study that has discussed the predictive power of a dataset. Perhaps a future research direction.

However, I did find an article published on R-bloggers that discussed about a predictive power score, a concept somewhat similar to correlation coefficient.

And finally something about mapping. I think a better term could be "correlation" which at least quantifies the relationship between two variables X and Y.

References

1. Lee, P. H. (2014). Resampling methods improve the predictive power of modeling in class-imbalanced datasets. International journal of environmental research and public health, 11(9), 9776-9789.
2. López‐López, J. A., Marín‐Martínez, F., Sánchez‐Meca, J., Van den Noortgate, W., & Viechtbauer, W. (2014). Estimation of the predictive power of the model in mixed‐effects meta‐regression: A simulation study. British Journal of Mathematical and Statistical Psychology, 67(1), 30-48.
3. Newson, R. B. (2010). Comparing the predictive powers of survival models using Harrell's C or Somers’ D. The Stata Journal, 10(3), 339-358.

Rather than asking about the predictive power of a dataset, I think it's intuitive to ask about the predictive power of a model. My reasoning is as follows;

A dataset can be univariate, bivariate or multivariate types. The dataset can contain only numerical features or categorical features or both. Suppose there is a univariate dataset with a negative skewed distribution. In such a case the mean, median will be less than the mode. Now suppose this univariate dataset consist of continuous data type. Knowing that its distribution is negatively skewed has already given the analyst a clue about its symmetry or distribution. So basis of this brief introduction, as an analyst will I be interested to know the predictive power of a dataset or the model('s) that I build using this dataset, is a question worth discussing?

There have been several studies in literature that have discussed the model's predictive power like 1,2,3 (see references). In contrast, I have not come across any study that has discussed the predictive power of a dataset. Perhaps a future research direction.

However, I did find an article published on R-bloggers that discussed about a predictive power score, a concept somewhat similar to correlation coefficient.

And finally something about mapping. I think a better term could be "correlation" which at least quantifies the relationship between two variables X and Y.

Note

A similar question was asked on stats.stackexchange.com. The comments in it conform to my initial doubt, that there is no such thing as the predictive power of a dataset.

References

1. Lee, P. H. (2014). Resampling methods improve the predictive power of modeling in class-imbalanced datasets. International journal of environmental research and public health, 11(9), 9776-9789.
2. López‐López, J. A., Marín‐Martínez, F., Sánchez‐Meca, J., Van den Noortgate, W., & Viechtbauer, W. (2014). Estimation of the predictive power of the model in mixed‐effects meta‐regression: A simulation study. British Journal of Mathematical and Statistical Psychology, 67(1), 30-48.
3. Newson, R. B. (2010). Comparing the predictive powers of survival models using Harrell's C or Somers’ D. The Stata Journal, 10(3), 339-358.