NOAA’s climate normals data for 1981-2010 includes the standard deviation of high and low daily temperatures. I don’t know if you’ve studied statistics, but basically the higher the standard deviation, the higher the variation. About 68% of days should have temperature within one standard deviation of the mean, for example. Unfortunately I am not aware as NOAA putting out anything so nice and readable as a histogram, and the data is hard for a human being to read.

First you have to know the station code. You can consult a list like this one to find that the code for Denver-Stapleton is USW00023062. Next you consult this table of the standard deviation in the daily high temperatures. Use ctrl-f to find the first instance of USW00023062, which is the start of the data for Denver-Stapleton. The “01” stands for January, and the numbers after that (133C 133C 133C 132C etc) stand for ten times the standard deviations of the daily high temperature in degrees Fahrenheit for Jan 1, Jan 2, Jan 3, Jan 4, etc. In other words, the standard deviation in the normal daily high for Jan. 1 at Denver-Stapleton is 13.3 degrees Fahrenheit. Don’t be fooled by the “C”. It doesn’t mean Celcius or Centigrade, but “complete”, meaning that there is no missing data for that date. If there’s an S, R, P, or Q instead of C that means there is less than 30 years of data for that date. To find the data for Dec. 25, go down to where is says “USW00023062 12” (for Denver-Stapleton December) and across to the 25th entry after that to find the standard deviation is 13.4 degrees Fahrenheit. If daily high temperatures are normally distributed (i.e., fit a symmetrical bell curve), you would expect a Christmas day 26.8 degrees warmer than average (2 standard deviations) about once every 50 years and one Christmas day 26.8 degrees colder than average in the same time period.

Now you can compare that to the Minneapolis-St. Paul Airport (station code = USW00014922) and find that the standard deviation there is 12.2 degrees Fahrenheit. So there is less variation in temperature on Christmas day in Minneapolis than Denver but not by a huge amount. They are quite similar to each other compared to the radically lower standard deviation in San Francisco, which is only 4.2 degrees.

NOAA has many other datasets than standard deviation in the daily high temperature. See this page for a list but to make any sense out of the abbreviated file names, you need to consult this readme doc.