Most summers are now either hot or extremely hot compared with the mid-20th century, researchers have found.

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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.

James Hansen, a retired NASA climate scientist and professor at Columbia University, and two colleagues compared 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.

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

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

For each time period, 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.

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.