One feature of data that you may want to consider is that of time. A graph that recognizes this ordering and displays the change of the values of a variable as time progresses is called a time series graph.

Suppose that you want to study the climate of a region for an entire month. Every day at noon you note the temperature and write this down in a log. A variety of statistical studies could be done with this data. You could find the mean or the median temperature for the month. You 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 you have collected.

Since each date is paired with the temperature reading for the day, you don‘t have to think of the data as being random. You can instead use the times given to impose a chronological order on the data.

## Constructing a Time Series Graph

To construct a time series graph, you must look at both pieces of the paired data set. 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 you 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 on indefinitely. These cyclical patterns are also easy to see with a time series graph.

## An Example of a Time Series Graph

You can 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**

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 |