Today's blog post was originally published last year:
Yesterday's blog post talked about travelling the country, visiting places that had a normal monthly temperature of 70 degrees. According to the
National Centers for Environmental Information:
What Are Climate Normals?
Scientists traditionally define a Climate Normal as an average over a recent 30-year period. Our most recent installment
covers the period from 1981 to 2010. Why 30 years? Close to a century
ago, the International Meteorological Organization—now known as the World Metrological Organization (link is external)—instructed
member nations to calculate Climate Normals using 30-year periods,
beginning with 1901–1930. Also, a general rule in statistics says that
you need at least 30 numbers to get a reliable estimate of their mean or
average. So, our scientists have traditionally defined Normals as
averages over 30 years simply because that is the accepted
convention—not because a 30-year average is the only logical or “right”
way to define a Climate Normal.
A bell shaped curve is called a normal curve and according to the
Central Limit Theorem in statistics:
The Central Limit Theorem (CLT for short) basically says that for
non-normal data, the distribution of the sample means has an
approximate normal distribution, no matter what the distribution of the
original data looks like, as long as the sample size is large enough
(usually at least 30) and all samples have the same size. And it doesn’t
just apply to the sample mean; the CLT is also true for other sample
statistics, such as the sample proportion. Because statisticians know so
much about the normal distribution, these analyses are much easier.
So, your data can approximate a normal curve if you have at least 30 data items.
According to their data, the "normal" high temperature for
October 17th in Modesto, CA is 78.7 and the predicted high was 82 degrees. As we talked about on
Monday,
the average, or mean, gives only half the information. We also need the
standard deviation, which is not included with the normal temps. But
since our high today is only a little more than 3 degrees from the mean,
we can probably safely assume that it's a reasonably "normal" value.
The
normal temperature for today (it's the 17th as I'm writing this) was
found by taking the average of the high temperature on this day every
year between 1981 and 2010. The normal high for the month is the average
of the high temperatures for each day of the month. Here are the
monthly "normal" highs for Modesto:
| Jan |
Feb |
Mar |
Apr |
May |
Jun |
Jul |
Aug |
Sep |
Oct |
Nov |
Dec |
| 55.4 |
63.8 |
68.7 |
74.7 |
82.9 |
89.9 |
95.1 |
93.6 |
89.0 |
79.0 |
65.5 |
55.6 |
The average annual temperature is 76.1
degrees and the standard deviation is 14.3 degrees, which says that
about two-thirds of the months should have an average high temperature
between 61.8 and 90.4 degrees, which they do. We can say something like
"The monthly high temperatures range from a low of 55 degrees in
January, to a high of 95 degrees in July. Eight months of the year have
an average high temperature between 62 and 90 degrees".
Meanwhile, in International Falls, MN, the average annual temperature is 48.7 degrees and the standard
deviation is 23.1 degrees, which says that about two-thirds of the
months should have an average high temperature between 25.6 and 71.8
degrees, which they don't.
| Jan |
Feb |
Mar |
Apr |
May |
Jun |
Jul |
Aug |
Sep |
Oct |
Nov |
Dec |
| 15.4 |
22.0 |
34.7 |
51.5 |
64.8 |
73.2 |
77.8 |
75.9 |
65.4 |
51.1 |
33.7 |
19.0 |
We
can say something like "The monthly high
temperatures range from a low of 15 degrees in January, to a high of 78
degrees in July. Six months of the year have an average high
temperature between 26 and 72 degrees". In this case, the median would
make a better measure. The median is 51.3, Q1 is 30.8 and Q3 is 67.4.
Fifty percent of the values will fall in between Q1 and Q3. Or 6 values
should fall between 31 and 67 degrees, which they do. Since there are
only 12 data items, we don't really have a normal distribution in either
case. It's just that Modesto was a little better behaved. Here's a
graph of the monthly high temperatures, with Modesto in
red and International Falls in
blue.
So, now you know what normal means. At least as far as temperature goes.
Interesting days
Today -
Get Smart About Credit Day,
Chocolate Cupcake Day,
No Beard Day and
Conflict Resolution Day
Tomorrow -
Evaluate Your Life Day
Next Thursday -
International Artists Day,
Sourest Day,
Punk for a Day Day,
Greasy Food Day and
World Pasta Day
November 18 -
Apple Cider Day,
Vichyssoise Day,
Princess Day,
Adoption Day,
Human-Animal Relationship Awareness Week,
Occult Day,
Housing Day,
Mickey Mouse Day and
GIS Day
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