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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
 Year Population 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

Courtney Taylor