Pinnacle Environemtal & Earth Sciences

(ISSN: 2360-9478)

November 2017, Vol. 4 (1).

© Author(s) 2017. This work is distributed under the Creative Commons Attribution 3.0 License.

Research Article


Non-normal Distribution of Temperatures in the United States of America during 1895-2016: A Challenge to the Central Limit Theorem

Hector Adolf Quevedo Urias1*, Gabriel A. Gonzalez2

1*Department of Civil Engineering and Environmental,
Engineering,Institute of Engineering and Technology,
Universidad Autonoma de Cd. Juarez, Mexico.

2Department of Chemistry,
El Paso Community College, U.S.A.

Accepted 16 November, 2017; Available Online 24 November, 2017.


Statistical arguments show the mean annual temperatures of the United States do not follow the precepts of the Central Limit Theorem (CLT). Calculations of descriptive statistics provided results with a skewness value of .6548 and of kurtosis value of .494 showing a substantial variation of the data suggesting that the temperatures do not follow a normal distribution. We constructed normal probability graphs utilizing the Anderson-Darling goodness of fit test to confirm the normality of the data obtaining an A-D value of 1.716 and P < .005 indicating the mean annual temperatures are not symmetrical. Calculations of density probabilities proved that the configuration of the density probability graph is skewed to the right due to the variation of the temperature values, thus, asymmetrical. Calculations of the objective and subjective evaluations of the temperature values by using a quadratic model yielded an objectivist diagnostics of R2 = 31.7%, PRESS = 81.59, VIF (Variance inflation factor) = 16.5 and the Durbin-Watson = 1.537. Besides, the subjective residual graphs revealed the temperature data is far from normal. Our results indicate the United States mean annual temperature values are challenging the suppositions of the CLT.

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