[Normal_gaussian]

ML + Big Data are a specific application of statistics

To to do anything beyond use tools other people have made (and never be sure whether results are meaningful or not) statistics are required

Of course, to make money from the ML boom you can probably get away with coincidence and correlation

[bitL]

Statistics means aggregate stuff and uses simplified characteristics out of semi-structured data. ML + Big Data allows you to ask precise questions like Where? How? Which ones?

[nfoz]

As user "highd" suggested, I think you are confusing two words. I refer to Wiktionary for definitions:

Statistics: A mathematical science concerned with data collection, presentation, analysis, and interpretation.

Statistic: A quantity calculated from the data in a sample, which characterises an important aspect in the sample (such as mean or standard deviation).

If "statistics" is the term for taking a mathematical approach to understanding data, then "machine learning" is basically an applied subset of that. But you seem to be specifically using the "a statistic" definition to describe what you think the "study of statistics" is entirely concerned with.