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Data Set #049

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About the Data

    An important class of distributions or density curves in statistics is the normal distribution.  All normal distributions have the same overall shape that is often referred to as "bell shaped".  These shapes are symmetric about the center, which is the location of the mean, median and mode of the data set.   It appears that the precipitation frequency distribution for Reading is "almost normal" since it is almost symmetric about the center and has a bell-shaped appearance.  If students were to display precipitation distributions for other cities, many of these would also have the same bell-shaped curve. Why is this so?  The answer lies in the fact that precipitation amounts, like many other natural phenomena, are the result of many random factors. When this is the case, we expect a normal distribution.

    Mentioned above was the fact that the center of a normal distribution is the mean.  The mean annual precipitation for the years 1863 to 2006 was 42.1 inches, which looks about right on the histogram.   It's quite obvious that the center (mean) for the Reading distribution would be quite different than the center for a much drier city such as Salt Lake or Phoenix.  Also,  a city whose precipitation from year to year is more consistent or more varied would have a histogram that is narrower or wider, respectfully.  So even though normal distributions have the same overall shape, they may have different centers (means) and have different widths (deviations from the mean).  The width of a normal distribution is quantified by computing the standard deviation. For the Reading data, the standard deviation is 6.9 inches.  (The formula to compute this number is not given here, but can be found in any basic statistics text.  Also, most calculators, spreadsheets and statistics packages will compute the standard deviation.)

    If we denote the mean by m and the standard deviation by s, then any normal distribution can be described by the 68-95-99.7 rule.  This rule states that:  68% of the data will lie within 1s of the mean m, 95% of the data will lie within 2s of the mean m, and 99.7% of the data will lie within 3s of the mean m . We can use the 68-95-99.7 rule as a means to check "how normal" the precipitation data are for Reading.  This is a good student exercise.  We can also use properties of the normal distribution to answer a question such as, "How likely is it that the precipitation for Reading will be between 30 and 31 inches in any given year?".  Details are left for statistics courses.

We obtained these and other precipitation data from the United States Historical Climate Network (USHCN), part of NOAA's National Climate Data Center.  For more recent precipitation and temperature values, go to DataSet#050.

Data source: United States Historical Climate Network (USHCN)
http://www.ncdc.noaa.gov/ol/climate/research/ushcn/ushcn.html

       
     
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Reading, Pennsylvania Annual Precipitation

     

Source: US Historic Climate Network

     
         

year

precipitation (in.)

 

Bin

Frequency

1863 47.73   26-30 2

1864

39.14   30-34 17

1865

50.46   34-38 20

1866

42.10   38-42 39

1867

49.83   42-46 28

1868

49.09   46-50 20

1869

50.01   50-54 13

1870

49.74   54-58 2

1871

46.23   58-62 2

1872

40.75   62-66 1

1873

58.28      

1874

36.89   Mean 42.10

1875

41.40   Median 41.55

1876

39.92   Standard Deviation 6.86

1877

45.53      

1878

37.17      

1879

41.78      

1880

31.35      

1881

40.35      

1882

39.97      

1883

40.76      

1884

48.60      

1885

38.82      

1886

40.57      

1887

42.59      

1888

51.97      

1889

64.69      

1890

46.43      

1891

48.63      

1892

36.33      

1893

38.61      

1894

51.99      

1895

33.30      

1896

33.50      

1897

48.60      

1898

46.03      

1899

44.66      

1900

35.19      

1901

44.34      

1902

52.26      

1903

45.84      

1904

41.84      

1905

38.35      

1906

43.84      

1907

43.78      

1908

36.16      

1909

32.34      

1910

34.67      

1911

45.14      

1912

47.09      

1913

43.41      

1914

31.15      

1915

44.10      

1916

41.66      

1917

33.12      

1918

34.28      

1919

41.30      

1920

38.20      

1921

35.77      

1922

33.96      

1923

31.48      

1924

41.56      

1925

40.04      

1926

39.89      

1927

35.61      

1928

40.29      

1929

40.56      

1930

26.08      

1931

32.54      

1932

44.49      

1933

44.24      

1934

44.78      

1935

37.61      

1936

42.17      

1937

41.54      

1938

43.40      

1939

40.43      

1940

40.06      

1941

31.39      

1942

53.73      

1943

33.08      

1944

41.96      

1945

49.48      

1946

37.35      

1947

45.41      

1948

48.23      

1949

38.52      

1950

42.64      

1951

44.16      

1952

55.55      

1953

50.83      

1954

35.65      

1955

43.28      

1956

44.96      

1957

31.68      

1958

44.87      

1959

36.27      

1960

39.97      

1961

39.47      

1962

40.98      

1963

33.54      

1964

33.84      

1965

27.33      

1966

34.44      

1967

39.16      

1968

34.91      

1969

39.23      

1970

37.47      

1971

45.95      

1972

53.63      

1973

51.06      

1974

39.34      

1975

53.50      

1976

42.97      

1977

43.46      

1978

44.13      

1979

48.61      

1980

32.95      

1981

34.62      

1982

41.12      

1983

50.42      

1984

49.08      

1985

40.14      

1986

45.89      

1987

39.85      

1988

38.32      

1989

47.24      

1990

46.00      

1991

35.76      

1992

39.08      

1993

47.78      

1994

49.18      

1995

40.16      

1996

60.46      

1997

33.31      

1998

41.89      

1999

36.58      

2000

30.22      
2001 35.15      
2002 45.51      
2003 56.32      
2004 52.62      
2005 49.90      
2006 52.26      
 

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