There is nothing normal about average, not when considering weather, anyway. Particularly here in the Northern Great Plains, the weather is not “supposed” to be average or even near average. The weather goes from above to below average all the time and sometimes by a lot.
In fact, what we call average is always changing. Our weather and climate are not static. It gets colder and it gets warmer. It gets wetter and it gets drier. These things vary day by day, month by month, year by year, century by century, and so on, without ever evening out.
A cold spring might be followed by a warm summer, but it does not cause it. In fact, the accepted, so-called “climate normals” are actually the average of the previous complete three decades. Every 10 years, what we call “normal” or “average” is adjusted to reflect the latest decade in order to remain somewhat current.