average january
temperatures
across the US

this data >>
was taken from a sample of 56 cities in the US.  every year for 30 years, the average daytime temperature for the month of january was recorded in each city.  the y-axis indicates how many cities fall into the 'categories' on the x-axis.

individual values ranged from 0° all the way up to 65° -  with the mean at about 26.49°F.

50% of the data lies between 18° and 34° and the two highest values (58° and 65°) can be considered outliers.

the data can be considered a normal distribution:  when plotted as a histogram, it roughly follows a bell curve- with a distinct peak towards the center and a symmetric shape. 

the bell curve:

<< a smooth curve can be used to illustrate the overall shape of the distribution.

the majority of the data is within 1-2 standard deviations from the mean.

* the standardized score (z-score) of seattle is 1.34 (18.09°F above the mean).

at 44°F, seattle is 18.09°F above the mean temperature.  this puts us at the 90.1 percentile mark.  this is particularly interesting because while we consider seattle to be a pretty cold place in january, we usually don't realize that we are warmer than about 90% of the rest of the of the country.

when scores are transformed from a normal distribution into standardized scores (z-scores), they are changed from being proportionate to a specific number to being proportionate to a mean of zero.  the shape of the distribution remains the same.