The Problem with Averages in Understanding Guns, Violence, and Crime (Take 3)

On the occasion of my 5th blog-iversary recently, I listed my 10 most popular blog posts ever. To my surprise, my 9th most popular blog post ever was published just 2 months ago, which means it got strong immediate readership. It was my second take on what I have called “The Problem with Averages in Understanding Guns, Violence, and Crime.”

The heart of the problem is that averages, as summary statistics, can obscure significant underlying differences in the data producing the averages. Two very different distributions of data can result in the same average. Imagine a city that has two neighborhoods and a city-level average of 100 homicides per year. That average is the same whether those homicides are distributed evenly between the two neighborhoods or are concentrated entirely in one of the two neighborhoods. The average as a summary statistic only tells part of the story.

Although I came to this insight inductively, through my own personal experience of living in a community with tremendous social inequality (including inequalities of violence and crime), others have approached the dangers of summary statistics in a much more sophisticated manner. Among these sophisticated thinkers are the statistician Francis Anscombe who in 1973 created four datasets with differing underlying data distributions but the same summary statistics (mean, standard deviation, and correlation).

By Anscombe.svg: Schutz derivative work (added English title using Inkscape): Avenue (Anscombe.svg) [GPL (, via Wikimedia Commons
Anscombe’s Quartet has recently been updated in a very clever way by two researchers at Autodesk (with an assist to Alberto Cairo). They show even more dynamically than Anscombe how different underlying distributions of data can yield the same summary statistics (h/t to Dan Hirschman at scatterplot).

“Same Stats, Different Graphs” from

To bring this back to guns, violence, and crime, over 2 years ago (April 10, 2015) I observed:

The problem with averages is that there is no “United States of America” when it comes to guns, violence, and crime, but many Americas. Some of these Americas – like my neighborhood in Winston-Salem – are more like our first world counterparts in the OECD, and some of them are more like the third world politically, economically, and socially.

I recently came across a graphic published by Richard Florida on The Atlantic magazine’s CityLab website in 2013 which makes my point in a visually compelling way by comparing the firearm homicide rates in various U.S. cities to those in comparable countries. For example, Phoenix’s homicide rate of 10.6 is like Mexico’s rate of 10, Buffalo is like Panama, Boston like Nicaragua, Atlanta like South Africa, Portland like Chile, and so on. Really fascinating and instructive.

Of course, what is missing here is the flip side of the coin. Those parts of the United States whose lower firearms homicide rates resemble those of European countries. Maybe someone who is better at data visualization than I am will undertake to create this second map?


  1. Hillary Clinton is lying about gun violence. There’s is no such a thing as “epidemic”. Crime and violence are sticky; they’re hyperconcentrated in a small number of places, people, and behaviors.

    She once again earns not 4 Pinocchios but at least 10.


    • What she is lying about (or is clueless about–I suspect the former) is what kind of epidemic. As Andrew Papachristos has mentioned, a lot of gun violence is epidemic as in the AIDS epidemic, i.e., you have to be intimately involved in the violence culture to get shot just as you had to be intimately involved in gay or IV sex to get AIDS. You couldn’t get AIDS with a sneeze and you don’t go around shooting or getting shot just because you own guns. In parts of New Mexico, the problem is a violent culture infected with drugs, alcohol, and poverty. Add guns and it gets worse.

      I would suspect in large part the same goes for suicide. There are reasons some areas of the nation have higher suicide rates. Gun availability correlates but so does SAD (esp. Alaska) and probably isolation and economic depression.

      As far as epidemics, obesity and type II diabetes kill ten times as many and that is, like suicide, self inflicted. Maybe that’s why Mike Bloomberg is going after both sugary drinks and guns.

      It is patently disingenuous to detach the discussion of firearms from lethal violence in the US. After all, we don’t fight wars with swords and archery equipment any more. Guns are more lethal than clubs or knives given their reach (and as is said, Sam Colt made all of us equal) and when misused, are social problems. We can offer solutions, which might be more useful than more food fights across the gun control no-man’s land.


  2. Some observations. “Average” really doesn’t exist until the data is all collected. In the middle of things, ‘average’ means very little.

    “Average” can be deceptive. If, in a particular location and situation, one has only a .01 percent chance of being injured (violent attack, car accident, lightening, saber-tooth squirrel attack) that percentage means very little to one who is injured in such fashion.

    “Gun Violence”. One wonders why “gun violence” is the only form of violence which can be combatted by legislation? Seemingly, “blunt instrument violence”, “fist violence” “kitchen knife violence” and “thrown rock violence” cannot be prevented by legislation. Why is that?


  3. In college I took two statistics courses that were labeled as junior/senior level. The instructor told us at the beginning they were senior/post graduate level. The main thing I took away from that was to never really trust any public quoted average without knowing something about it.

    When we would take a test after the professor was done he would give his answer. He would then ask who else had his. Usually it would be a third to half. He would then ask what everybody else got. Someone would give out an answer. He would ask if anybody else had that. There always was a few that did. He would then ask them to put there work up on the board. After he would turn to the rest of us and ask, “Does that look good to all of you?” If so, it was graded right.

    Always remember that statistics has a math symbol for ‘this is as close as I can get to and answer.’ So the average you see might be different yet equally correct if you did the math.


  4. What do you think of the research cited by Armed with Reason that says that guns are not as effective as knives or bats or running away? Now that seems fishy to me, but that alone won’t make them wrong.


    • Finding credible work on either side of the great gun debate takes work. Like I said above, if knives or bats were more effective than guns, do you suppose we would arm our military with guns, which cost way more than a Louisville Slugger? Running away doesn’t always work either. If my home is invaded, I prefer to have options other than running away.

      I prefer to find sources that are peer-reviewed when possible. Even that doesn’t guarantee anything is good science (e.g., the Kalesan et al Lancet paper, March 2016), given that so few folks are both unbiased and knowledgeable about the subject.


      • The thing that has worried me about Armed with Reason is that it seems like a lot of the work they cite IS peer-reviewed. (Then again I got kinda scared off by it and didn’t really look so maybe I’m just dumb)


    • This sounds like an article I assign in my class which is more complicated than the typical GVP takeaway. My problem with Armed with Reason is they already have their minds made up so they only look at conclusions from research that support their views. As do many pro-gun people.

      Liked by 1 person

      • And yeah, I’ve noticed a lot of their work is stuff by David Hemenway. That isn’t genetic fallacy, just saying that he HAS said stuff about firearms owners, and seems to have his mind made up(whether that influences his research or is because of his research idk)


      • Exactly, David. I commented recently on how AWR left out some key elements of a discussion and set up a straw man argument that was easy to push down. Likewise, the Kalesan piece strained to find correlations, including suggesting there was a correlation between ammo checks and gun violence. Even though, as someone later pointed out, the ammo check law had not been implemented.


      • Btw David, this is an awesome site. It brings something different. It’s not an echo chamber, and even the commenters are insightful and intelligent. Thank you and keep up the great work!!


      • Also something you might like David. Evan DeFillipis really seems to look up to someone you are probably quite familiar with. One of the most well known of the New Atheists, Sam Harris. I find that funny. You?


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