Data Home | Math Topics | Environment Topics | Topics Matrix | Master List | Help
 Download the Data RichText File Excel File Text File Minitab File (USHCN data from 2004) Data Set #049 About the Data View the Data Help with Using Data Play with the data on StatCrunch

Go to Top

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 precipitation data for the lower 48 states from the United States Historical Climate Network (USHCN), part of NOAA's National Climate Data Center. The USHCN has historical records for 1221 weather station in the lower 48 states, of which 1182 are currently operational.  At the USHCN website one can download historical data sets that have varying amounts of editing. We downloaded the (gigantic) national precipitation data, selected the Filnet edited data, then divided the national data set into state-by-state sets.    Note:  The Filnet edited precipitation data  (1) has removed outliers more that 3 standard deviations from the period mean (2) has been adjusted to remove time of observation bias, the Maximum/Minimum Temperature System (MMTS) bias, station moves/changes bias and (3) contains estimated values for missing/outlier data.

Tthe USHCN provides weather station information (referred to as the Station Inventory information), with details about station location, history, measuring devices, personnel, reliability, etc.   We edited this file on a state by state basis to include only latitude, longitude, and elevation data for the latest location of each station.   To download state-by-state files, go to DataSet#050.  Those wishing to obtain a single national or unedited file should go to the USHCN website.

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

Go to Top

View the Data

 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

Go to Top