Quick Answer: Around 45 KB per day of data usage/internet in background.

PI Network

Pi Network (PI) cryptocurrency is the first coin that can be mined through your mobile phone. It was launched on March 14, 2019, as a beta version by Stanford graduates, Dr Nicolas Kokkalis, Dr Chengdiao Fan, Aurelien Schiltz, and Vincent McPhillips. Since its inception, March 14 has been marked as PI day.

Their mode of approach was through building an app capable enough to gain users with interests in joining a new social network while mining cryptocurrency. 

Explaining The Mining of Cryptocurrency

Mining of cryptocurrencies like Bitcoin is increasingly hard and at this point you will spend more money on electricity than the reward of selling a Bitcoin if you find one. Contrary to usual cryptocurrencies with PI you can mine on your mobile phone. This is possible because it uses the Stellar Consensus Protocol in background.

Mining PI For Users

To mine Pi, all you have to do is install the PI app on your smartphone. The app connects to the node(s) and checks if transactions have been recorded on the ledger. The app connects to multiple nodes to cross-check this information. In Pi once a day everyone who contributed get a meritocratic distribution of new Pi by just being in the network. But this means that you have to be connected to the internet in order to mine Pi.

How much internet does it use?

So after mining Pi for a month every day without missing any days and staying connected for 24/7. My mobile phone has logged that the Pi app has used only 1.07 mb from Feb 28 to March 24, which is roughly 24 days. Making the total usage per day to 45 KB which really negligible in my opinion! So what are you waiting for? Mine away! https://minepi.com/