What do you mean by 'variety'?
One of the reasons big data systems took off was because enterprises had exports out of third party systems that they didn't want to model since they didn't own it. As well as a bunch of unstructured data e.g. floor plans, images, logs, telemetry etc.
It means that data comes in a ton of different shapes with poorly described schemas (technically and semantically).
From the typical CSV export out of an ERP system to a proprietary message format from your own custom embedded device software.
So AI currently, probably ;)