Lesson

A time series is a special kind of graph that records successive measurements made over a period of time. It may be a series of seconds, minutes, hours, days, weeks, months or years, just to name a few. We often (but not always) draw graphs of time series data as line graphs that can be used to make predictions and draw conclusions. We read a time series data graph just like we would a line graph.

Let's look through some examples now to see this in action.

The graph below shows the maximum temperatures in Sydney and Auckland for the first ten days of January 2014.

Determine whether each of the following statements are true or false.

a) Sydney was warmer on the 6th of January than it was on the 4th.

Do: On the 6th, Sydney's maximum temperature was $31^\circ$31°. On the 4th, Sydney's maximum temperature was $26^\circ$26°. So this statement is true.

b) Auckland was warmer on the 6th of January than it was on the 4th.

Do: On the 6th, Auckland's maximum temperature was $22^\circ$22°. On the 4th, Sydney's maximum temperature was $26^\circ$26°. So this statement is false.

c) On average, Sydney was warmer than Auckland.

Do: Let's do some calculations!

$\text{Average (Sydney)}$Average (Sydney) | $=$= | $\frac{28+36+28+26+29+31+22+22+24+28}{10}$28+36+28+26+29+31+22+22+24+2810 |

$=$= | $\frac{274}{10}$27410 | |

$=$= | $27.4^\circ$27.4° | |

$\text{Average (Auckland)}$Average (Auckland) | $=$= | $\frac{24+23+26+26+24+22+25+24+20+22}{10}$24+23+26+26+24+22+25+24+20+2210 |

$=$= | $\frac{236}{10}$23610 | |

$=$= | $23.6^\circ$23.6° |

This statement is true.

d) There was less fluctuation in Auckland's temperature than Sydney's temperature.

Do: The range is Sydney's maximum temperatures was $14^\circ$14° ($36-22$36−22). The range is Auckland's maximum temperatures was $6^\circ$6° ($26-20$26−20). So this statement is true.

e) This graph tells us why Sydney was warmer than Auckland on average.

Do: This graph only displays the temperatures. It doesn't give us any reasons for the temperature changes, so this statement is false.

f) There are only two out of the ten days when Auckland was warmer than Sydney.

Do: This statement is true. The maximum temperature in Auckland was only warmer than Sydney on the 7th and 8th of January.

Determine whether each of the following statements are true or false.

There was more ice in 2007 than there was in 2005.

True

AFalse

BTrue

AFalse

BFrom the data it seems that as time passes there is less and less areas of ocean with at least $15%$15% sea ice.

True

AFalse

BTrue

AFalse

BThe Arctic sea ice extent is always greater at the end of any given year than in the middle of the year.

True

AFalse

BNot enough information.

CTrue

AFalse

BNot enough information.

CIt is coldest in the Arctic in September.

True

AFalse

BTrue

AFalse

B

The graph shows the change in Apple Inc.'s share price along with major releases of its products. From the graph, determine whether each of the following are true or false.

The price of Apple’s products always increased.

True

AFalse

BTrue

AFalse

BThe release of Apple products promoted a general trend upwards in the share price.

True

AFalse

BTrue

AFalse

BApple’s share price increased by the same amount each year.

True

AFalse

BTrue

AFalse

B

Plan and conduct investigations using the statistical enquiry cycle: A justifying the variables and measures used B managing sources of variation, including through the use of random sampling C identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays D making informal inferences about populations from sample data E justifying findings, using displays and measures.

Investigate a given multivariate data set using the statistical enquiry cycle