When playing the video in the background, the YouTube app used about 4MB.
When playing the same video in the foreground, the YouTube app used about 24MB.
By default, YouTube selected the highest video quality that was available for this video: 480p.
This means that you can save bandwidth by playing music videos in the background. YouTube uses separate chunked streams for audio and video, so it can download only audio files when playing videos in the background.