Variance in Science is the square of the standard deviation. Since you are talking about a scientific issue, and discussing measurements, and since you claim to have a BSc it is reasonable to expect the word to be used in a technical context.

All history is recorded history BY DEFINITION.

You shouldn't be waving your degree around, you plainly are not a scientist.

As to your understanding of this, consider tossing a coin, and getting heads. For one coin it's a 1/2 chance. For 2 in a row it's 1/4. For 100 the chance is 1/(2^100) which is about 10^-30, a vanishingly small chance.

Now let's take the last 100 years of climate data from phoenix, we can estimate the chance of any day being over 100F from the data, and from that the chance of 100 days straight of over 100F.

Given that less than half of the time it's over 100F in Phoenix, the odds of having 100 days in a row over 100F is less than 10^-30.

This is 1st year science. Your very first data analysis course.