The scare quotes above are deserved. It's dubious, as Dan Nguyen points out in this thread, that The New York Times or The Guardian are representative of “the media” at large. “The media” is a fuzzy umbrella term that encompasses anything from national and local TV to online news startups —and, yes, also quality national newspapers. The two stacked bars on the right may look very different —even more skewed, perhaps— if we really surveyed the media.
On a side note, I agree with the authors of the report that journalism may bias our perceptions of the most common causes of death by overemphasizing unusual events, but I doubt there's an easy solution to that problem —or even that it is a problem at all. News media's preference for novelty and tragedy isn't really just news media's, but human nature's, and they reinforce each other in and endless loop.
Besides the real and intrinsic newsworthiness of unusual and tragic events —more about that in this article by Nieman and in the tweet below,— think about your conversations with friends and family: if you can choose between talking about the many people who die of heart disease or cancer every day, or the dozens who died in a recent terrorist attack, accident, or natural catastrophe, what do you think the result would be? And what would you read, listen to, or watch first, a piece about the former —the quotidian— or about the latter —the unique and dramatic?
Again, don't miss Dan's critique, particularly one of his latest tweets, darkly sarcastic but very on point:
OTOH...When have we, as a news industry stopped, gathered the data, and asked ourselves, “Does the math justify another story on a *minority* boy killed by cop? There’s a literal majority of us who live 60+ years w/o being shot, just to get literally genocided by heart disease..— Dan Nguyen (@dancow) May 31, 2019
