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 0Year | 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 |