What Are Time Series Graphs?

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

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

YearPopulation
190076094000
190177584000
190279163000
190380632000
190482166000
190583822000
190685450000
190787008000
190888710000
190990490000
191092407000
191193863000
191295335000
191397225000
191499111000
1915100546000
1916101961000
1917103268000
1918103208000
1919104514000
1920106461000
1921108538000
1922110049000
1923111947000
1924114109000
1925115829000
1926117397000
1927119035000
1928120509000
1929121767000
1930123077000
193112404000
193212484000
1933125579000
1934126374000
193512725000
1936128053000
1937128825000
1938129825000
193913088000
1940131954000
1941133121000
194213392000
1943134245000
1944132885000
1945132481000
1946140054000
1947143446000
1948146093000
1949148665000
1950151868000
1951153982000
1952156393000
1953158956000
1954161884000
1955165069000
1956168088000
1957171187000
1958174149000
1959177135000
1960179979000
1961182992000
1962185771000
1963188483000
1964191141000
1965193526000
1966195576000
1967197457000
1968199399000
1969201385000
1970203984000
1971206827000
1972209284000
1973211357000
1974213342000
1975215465000
1976217563000
197721976000
1978222095000
1979224567000
1980227225000
1981229466000
1982231664000
1983233792000
1984235825000
1985237924000
1986240133000
1987242289000
1988244499000
1989246819000
1990249623000
1991252981000
1992256514000
1993259919000
1994263126000
1995266278000
1996269394000
1997272647000
1998275854000
1999279040000
2000282224000