Extension work idea: using moving averages

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How students might explore the data.

Plotting a line graph of the annual average maximum temperature since 1900 gives this:

16

15

14

13

12

11

10

Year

Clearly, this has a lot of variability. Looking at the average for each decade produces the following.

1900-1909

1910-1919

1920-1929

1930-1939

1940-1949

1950-1959

1960-1969

1970-1979

1980-1989

1990-1999

2000-2009

Mean temperature

12.616

12.892

12.894

13.155

13.37

13.12

12.808

13.15

13.12

13.797

14.111

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16

15

14

13

12

11

10

18

17

16

15

21

20

19

24

23

22

This reduces the variability and may indicate an increasing temperature.

These graphs are for the annual average temperatures, but if we suspect that the summers are getting hotter and the winters are getting cooler, then it would make sense to consider them separately.

Summers and winters

Looking at the average value for summer each year – using June, July and August temperatures and the average value for winter each year – using December, January and February gives the following.

Mean Summer highs

Year

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1900-1909

1910-1919

1920-1929

1930-1939

1940-1949

1950-1959

1960-1969

1970-1979

1980-1989

1990-1999

2000-2009

Mean Winter lows

3

2

1

0

5

4

-1

-2

-3

-4

Year

Again, these graphs have a lot of variability by individual years.

Looking at decades may help give a clearer picture of trends over time… or not!

Summer high

19.17

19.39

19.11

20.02

20.09

19.68

19.30

19.86

19.77

20.50

20.56

Winter low

1.45

1.90

2.11

1.76

1.08

1.19

0.85

1.83

1.33

1.99

2.10

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2,50

2,00

1,50

1,00

0,50

0,00

21,00

20,50

20,00

19,50

19,00

18,50

18,00

Summer highs by decade

Decade

Winter lows by decade

Decade

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Exploring with Boxplots

Sample boxplots for mean annual temperatures for the decades (top to bottom):

1900-1909, 1910-1919 and then 1990-1999 and 2000-2009

Using the median value removes the effects of extreme values. This seems to give a clear indication of a general increase in temperature progressively over the decades shown.

Annual Precipitation by decade

Top to bottom: 1900-1909, 1910-1919 and then 1990-1999 and 2000-2009

There doesn’t seem to be any trend for precipitation shown when the data are analysed in this way.

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Extension work idea: using moving averages

Using 10 point moving averages gives a clearer indication that temperatures might be increasing.

Mean annual temperature

10 point moving averge

15

14,5

14

13,5

13

12,5

12

Year

2,5

2

1,5

1

0,5

0

Looking at the winter minimums and summer maximums:

Winter minimum

10 point moving average

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Summer maximum

10 point moving average

21

20,5

20

19,5

19

18,5

18

It seems as if the summers are getting warmer, but it’s not clear what’s happening with the winters.

1300

1200

1100

1000

900

800

700

600

Precipitation

Similarly, with precipitation it is difficult to ascertain whether it is static or not.

Annual Precipitation (mm)

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Using 10 and 100 point moving averages possibly show an increasing trend.

Annual precipitation

10 point moving average

960

940

920

900

880

860

840

Annual precipitation

100 point moving average

940

935

930

925

920

915

910

905

900

895

890

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