Extraordinarily hot summers — the kind that were virtually unheard-of in the 1950s — have become commonplace.

This year’s scorching summer events, like heat waves rolling through southern Europe and temperatures nearing 130 degrees Fahrenheit in Pakistan, are part of this broader trend.

The chart above, based on data from James Hansen, a retired NASA climate scientist and professor at Columbia University, shows how summer temperatures have shifted toward more extreme heat over the past several decades.

To create the bell curves, Dr. Hansen and two colleagues compared actual summer temperatures for each decade since the 1980s to a fixed baseline average. During the base period, 1951 to 1980, about a third of local summer temperatures across the Northern Hemisphere were in what they called a “near average” or normal range. A third were considered cold; a third were hot.

Since then, summer temperatures have shifted drastically, the researchers found. Between 2005 and 2015, two-thirds of values were in the hot category, and nearly 15 percent were in a new category: extremely hot.

Practically, that means most summers are now either hot or extremely hot compared with the mid-20th century.

1951 to 1980 2005 to 2015 1951-1980 Base period More frequent Hot Normal Extremely cold Cold Normal Extremely hot Extremely cold Cold Hot Extremely hot 1951 to 1980 2005 to 2015 More frequent 1951-1980 Base period Extremely cold Extremely hot Normal Extremely hot Extremely cold Normal 1951 to 1980 More frequent Hot Extremely cold Cold Normal Extremely hot 2005 to 2015 More frequent 1951-1980 Base period Hot Extremely hot Extremely cold Cold Normal 1951 to 1980 More frequent Extremely cold Normal Extremely hot 2005 to 2015 More frequent 1951-1980 Base period Extremely hot Extremely cold Normal

The big increase in summer temperatures under the dark red category of extreme heat is “right in line” with what scientists expect to see as the climate warms over all, said Todd Sanford, director of research at Climate Central, a nonprofit science and news organization.

For each time period above, the distribution of summer temperatures forms what is known as a bell curve because most measurements fall near the average, forming the bump – or bell – in the middle. More extreme temperatures, which happen less frequently, fall in the wings, with heat waves on the right and cold-snaps on the left.

As the curve’s average – the top of the peak – shifts rightward over time, more temperatures in more places end up in the hot and extremely hot categories and fewer end up in the cold category.

Dr. Hansen’s curves also flatten out, which some have suggested is an indication of greater temperature variability. But other climate scientists, including Zeke Hausfather, an energy systems analyst at the University of California, Berkeley, have pointed out that this effect is mainly a reflection that some parts of the world are warming faster than others. There is no evidence that temperatures are becoming more variable in most parts of the world after warming has been accounted for.