This article about an earthquake that hit Baja California uses numbers in a few ways to tell the story.
First of all, the quantifying units like 19 miles, 900,000 people, 100 miles and 18 years were used effectively. I don't think they're overwhelming at all. More than anything, they're necessary in some cases because the story is about an earthquake...numbers help people cognitively process how far loved ones might be from the epicenter of the quake. The reporter chose well to put these numbers into the story.
No math was used to crunch out numbers or anything like that. The numbers in this story relate directly to where the quake hit (19 miles southeast of the Mexicali border) and how many people are around the affected area (900,000 people). This is a straight fact block story, doling out the information un-analyzed.
The numbers come from seismologists analyzing the earthquake and institutional sources with population numbers but they aren't attributed to any one source in the story. These are just my assumptions as to where the reporter found them.