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Time Series Graphs

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Time Series Graphs

A time series graph of the population of the United States from the years 1900 to 2000.

C.K.Taylor

Suppose that we want to study the climate of a region for an entire month. Every day at noon we note the temperature and write this down in a log. A variety of statistical studies could be done with this data. We could find the mean or the median temperature for the month. We could construct a histogram displaying the number of days that temperatures reach a certain range of values. But all of these methods ignore a portion of the data that we have collected.

The feature of the data that we may want to consider is that of time. Since each date is paired with the temperature reading for the day, we don‘t have to think of the data as being random. We can instead use the times given to impose a chronological order on the data. A graph that recognizes this ordering and displays the changing temperature as the month progresses is called a time series graph.

Constructing a Time Series Graph

To construct a time series graph, we must look at both pieces of our paired data set. We start with a standard Cartesian coordinate system. The horizontal axis is used to plot the date or time increments, and the vertical axis is used to plot the values variable that we are measuring. By doing this each point on the graph corresponds to a date and a measured quantity. The points on the graph are typically connected by straight lines in the order in which they occur.

Uses of a Time Series Graph

Time series graphs are important tools in various applications of statistics. When recording values of the same variable over an extended period of time, sometimes it is difficult to discern any trend or pattern. However, once the same data points are displayed graphically, some features jump out. Time series graphs make trends easy to spot. These trends are important as they can be used to project into the future.

In addition to trends, the weather, business models and even insect populations exhibit cyclical patterns. The variable being studied does not exhibit a continual increase or decrease, but instead goes up and down depending upon the time of year. This cycle of increase and decrease may go own indefinitely. These cyclical patterns are also easy to see with a time series graph.

An Example of a Time Series Graph

We use the data set in the table below to construct a time series graph. The data is from the U.S. Census Bureau and reports the U.S. resident population from 1900 to 2000. The horizontal axis measures time in years, and the vertical axis represents the number of people in the U.S. The graph shows us a steady increase in population that is roughly a straight line. Then the slope of the line becomes steeper during the Baby Boom.

U.S. Population Data 1900-2000

0 0 0 0 0 0
YearPopulation
1900 76094000
1901 77584000
1902 79163000
1903 80632000
1904 82166000
1905 83822000
1906 85450000
1907 87008000
1908 88710000
1909 90490000
1910 92407000
1911 93863000
1912 95335000
1913 97225000
1914 99111000
1915 100546000
1916 101961000
1917 103268000
1918 103208000
1919 104514000
1920 106461000
1921 108538000
1922 110049000
1923 111947000
1924 114109000
1925 115829000
1926 117397000
1927 119035000
1928 120509000
1929 121767000
1930 123077000
1931 12404000
1932 12484000
1933 125579000
1934 126374000
1935 12725000
1936 128053000
1937 128825000
1938 129825000
1939 13088000
1940 131954000
1941 133121000
1942 13392000
1943 134245000
1944 132885000
1945 132481000
1946 140054000
1947 143446000
1948 146093000
1949 148665000
1950 151868000
1951 153982000
1952 156393000
1953 158956000
1954 161884000
1955 165069000
1956 168088000
1957 171187000
1958 174149000
1959 177135000
1960 179979000
1961 182992000
1962 185771000
1963 188483000
1964 191141000
1965 193526000
1966 195576000
1967 197457000
1968 199399000
1969 201385000
1970 203984000
1971 206827000
1972 209284000
1973 211357000
1974 213342000
1975 215465000
1976 217563000
1977 21976000
1978 222095000
1979 224567000
1980 227225000
1981 229466000
1982 231664000
1983 233792000
1984 235825000
1985 237924000
1986 240133000
1987 242289000
1988 244499000
1989 246819000
1990 249623000
1991 252981000
1992 256514000
1993 259919000
1994 263126000
1995 266278000
1996 269394000
1997 272647000
1998 275854000
1999 279040000
2000 282224000
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