Normal Temperatures

Recently, I started asking myself why every weather forecast gives us the average high/low for that day of the year. In actuality, I started trying to figure out if those were the conditions that I should expect if I walked outside a year from now.  You guys know me pretty well, so you have already figured out that it didn't stop there. So, I went to the "Weather Underground" website and starting digging into the archives there.

The first thing I found out is that you can get a lot of historical (high/low) data at various weather stations around the country.  The interface is a little clunky and I didn't feel like writing a script, but I did get all the data for January 1 at Drake Field in Fayetteville.  The site has the highs/lows for the station there for 1948-2010 (actually 1961-1972 are missing). I placed the data for January 1 at the "KFYV" weather station (72701) into a spreadsheet. Then, I started looking at all the available data from a descriptive statistical point of view starting with the high temperature.

Descriptive Statistics for the Maximum Temperature at Drake Field in Fayetteville, Arkansas (1948-2010):

• Number of Data Points: 51 (N)
• Maximum:  70 degrees F
• Minimum:  15 degrees F
  
• Mean:  45.98 degrees F
• Standard Deviation:  12.62 degrees F
  
• Skewness:  -0.3368
• Kurtosis:  0.0052
• Test for normality of the distribution cannot reject Normal Distribution as the null hypothesis.  This means that I "can" assume the data is normally distributed.

The histogram for the high temperatures plotted with a normal distribution is seen below.

I did the same thing for the minimum temperature.

Descriptive Statistics for the Minimum Temperature at Drake Field in Fayetteville, Arkansas (1948-2010):

• Number of Data Points: 51 (N)
• Maximum:  59 degrees F
• Minimum:  3 degrees F
• Mean:  26.45 degrees F
• Standard Deviation:  12.79 degrees F
  
• Skewness: 0.4511
• Kurtosis:  0.1077
  
• Test for normality of the distribution cannot reject Normal Distribution as the null hypothesis.  This means that I "can" assume the data is normally distributed.

 The histogram for the low temperatures plotted with a normal distribution is seen below.

Now, Weather Underground lists the average maximum temperature as 45 degrees F while the average minimum temperature is 26 degrees F.  If I truncate my averages (rather than round off), I get exactly those numbers. By now I am certain that you are wondering if my little exercise actually helped me figure out the initial question about what the weather conditions will be like on January 1, 2011. It did.  Today (January 12, 2010), I can say with 68% certainty that the high temperature on January 1, 2011 will be in the interval [33, 58] degrees F and the low temperature will be in the interval [14, 39] degrees F with 68% certainty.

I can hear Josh say, "Big deal, Russ!  You gave yourself a 25 degree window."  AND, he would be right.  However, that is my point.  When I started this meandering, I didn't realize how big the variation (i.e., the standard deviation) for those average temperatures really is.  SOOO, the next time the weatherman tells you that the high (or low) for the day is 12 degrees above normal (or below normal) you shouldn't be surprised (especially if you live in Fayetteville).