The Maryland Mall shooting, and other violent outbreaks already in 2014 bring to mind the following question: In the USA, are mass shootings becoming more frequent?

Unfortunately, according to the math, the gap between mass shootings is lessening over the years.

Let’s review what CNN reported recently, to answer these questions using a light touch of mathematics and statistics.

## Twenty-Four Major Shootings in the USA

The CNN article listed twenty-four shooting incidents that took place in the United States from 1966 through the end of 2013. Each time, at least 8 people were shot and killed by the perpetrator(s). In some cases, police shot and killed the gunman.

Let’s assume that CNN covered all the mass shootings that met the criteria of having at least 8 fatalities and occurred in the USA. Can we see any trends in their data?

## A Spreadsheet of Fatal Shooting Incidents

CNN had sorted these tragic events in descending order of the number of fatalities. However, we want to look for a trend over time. This spreadsheet is sorted chronologically, from oldest to most recent.

For our purposes, the three important columns are the date, the “# Killed”, and the “Days Since…”. That last column shows the spreadsheet’s calculation of the number of days between one incident and the next.

The CNN summary only provided the number of wounded for a three incidents.

A dozen of the shooters committed suicide to end their killing sprees. In 5 cases, the police shot and killed the perpetrator.

### A Graph of Shooting Deaths by Date

This graph summarizes the spreadsheet. The X-axis is the date of the shooting; the Y-axis is the number of victims killed in these incidents.

Remember that the data did *not* include events where fewer than 8 people were killed. We would have many more data points if it reported fewer fatalities per event.

One obvious trend is that the frequency has increased. The first 12 incidents were spread over 23 years; then there was a gap of about 5.5 years. The remaining 12 events occurred in the final 8.5 years.

However, the number of fatalities does not trend up or down. The data has a “floor” of 8 victims, due to the selection of the data. 10 of the 24 shootings had 8 victims. 7 incidents had either 10 or 11 victims. The graph shows that such incidents are spread throughout the whole time frame that CNN selected. The 2 incidents with the highest number of fatalities occurred in the final 8.5 years; but 3 earlier incidents claimed more than 15 deaths each.

### A Graph of the Frequency of Major Shootings in the USA

Let’s strip away the number of fatalities, so we can focus on the frequency of these major US shootings by plotting the number of days between incidents.

This graph illustrates the trend that these major shooting incidents have become more frequent in the USA.

This image also shows the spreadsheet calculations for the average and median values of the data for the “# Killed” and “Days Since…” columns.

The average (“AVG”) is simply the sum of the data, divided by the number of data points. The median is the value half-way through the data set as sorted by that criterion. Note that the median “# Killed” is the average of the 10 and 12 victims in the 12th and 13th incident, as sorted by the number of fatalities. Meanwhile, the average number of days between events is much larger than the median: over 2 years compared to under 1.5 years. This indicates that there were “a few” long gaps, but half the gaps were less than 435 days.

The standard deviation measures how “skewed” the values are. While the number of fatalities is somewhat spread out, there is a huge variation in the time elapsed between incidents.

### Summary and Conclusion for these Trending Statistics

We’ve used the data from a news article to look for trends in recent mass shootings in the United States.

The article had set a threshold for the data: that there would be at least 8 fatalities. CNN had reported 24 such incidents, with the dates and the number of deaths.

The graphs indicate that there is no particular trend towards having more or fewer fatalities in these events. One wonders, however, whether the number of wounded survivors has been increasing over time. That data was not reported in the CNN article.

One obvious trend is that the frequency of such incidents has risen in the past decade; more accurately, in the past 8.5 years. However, there had been some breaks as small as 1 or 2 months in the early 1980s. This makes it difficult to say that we live in more dangerous times.

Other factors which should be considered for a scholarly study is to correlate the data presented by CNN with the population of the USA over the same time periods. As well, the number of firearms owned by the public has, presumably, been increasing over the same time frame. Is there a relationship between the number of people, or the number of guns per person, and the increased frequency of mass shootings in the United States?

Lawrence says

Has anyone studied the affect of mass media on mass shootings? Does an increase in coverage result in more copycats? Are there other media “surges” that overshadow a mass shooting and result in less exposure and then there is a larger gap between incidents?

Murph says

It is good to see mass killings are down. I plugged in the data for mass killing using a threshold of 8, 10, 14, and 16, and those show mass killings are down both on 25 and 50 year trends

Down even more per capita.

And what is really good is the time gap between mass killings under any of those thresholds, except 12, increases year as well.,

Given any number defining mass shootings — except 12 — shows a decrease, I am curious as to why you picked 12???

Mike DeHaan says

Thanks for your comment. I apologize for not reviewing this article sooner.

I’m not sure about your question, “why did I pick 12” (deaths) to define mass shootings? My starting point was the CNN report, which had the threshold of 8 deaths in one incident. In the final graph, the average per incident was about 12.

In general, given a reasonably large set of data, it is usually possible to find that a sub-set of the data contradicts the major trend. That’s Simpson’s Paradox (or Yule-Simpson). I’m not sure that you found a Simpson’s Paradox in this report, but it’s possible.

Thanks for your note!