math statistics

Historical Temperatures Trends

 

In this project we will look at historical temperature records for several cities and use statistical methods to determine whether the data shows any significant patterns or trends in temperature over time.

 

The SPSS data file for the project, TempRecs.sav is posted on Piazza along with Excel version. The file contains the Annual Average Temperature records for two cities: New York, USA and Sydney, Australia. For each year, the annual average temperature value is calculated by averaging high temperature readings from every day of the year, observed in a specific location, Central Park for New York and Observatory Hill for Sydney.

 

In the project data file, three variables are recorded for each data point: the year (“year”), the Annual Average Temperature for Sydney (“Sydtemp”). The data are sorted by year in ascending order. For your convenience, Sydney temperatures have been converted to Fahrenheit.

 

Original data sources:

 

http://www.erh.noaa.gov/okx/climate/records/monthannualtemp.html (for NYC)

http://www.bom.gov.au/jsp/ncc/cdio/weatherData/av?p_nccObsCode=36&p_display_type=dataFile&_startYear=&p_c=&p_stn_num=066062 (for Sydney)

 

Exercise 1

1. a) Use SPSS to produce a scatterplot of the temperatures for New York City using the “year” as

x-axis.

1. b) Provide a paragraph describing whether you see any trends or patterns in the data from your

graph.

1. c) Produce a similar plot for Sydney.
2. d) In a paragraph, describe what you see for that city.
3. e) Describe any similarities and/or differences you observe between Sydney and New York City.

 

 

Extra Credit:

 

Online, find the temperature records for the city of your choice, the records have to go back at least 120 years. In one sentence, explain why you chose this specific city. Repeat Exercise 1 for your city.

 

 

Exercise 2

1. a) Use SPSS to find summary measurements for the annual average temperatures in New York

City over the entire recorded period (1869-2013): min, max, mean, median, mode, and

standard deviation.

Identify the hottest year and the coldest year.

 

 

 

 

1. b) Use SPSS to make a boxplot of the data set.
2. c) Repeat this exercise for the historical temperature values in Sydney.
3. d) Write a paragraph describing how the two cities differ in temperature. Hint: Base your answer

on any notable differences you observe in the two Box Plots.

 

Extra Credit: Repeat Exercise 2 for the city of your choice.

 

Exercise 3

1. a) Use SPSS to obtain the frequency distribution histogram of the annual average temperatures in

New York City. Describe the “shape” of the distribution.

1. b) Repeat the process for Sydney, using the same class limits you had for New York City.
2. c) In a paragraph, describe any similarities and differences you observe between the shapes of

the two distributions and interpret the meaning of these differences.

 

Extra Credit: Repeat Exercise 3 for the city of your choice.

 

 

Exercise 4A

Limit your attention to the most “recent” temperature data, (which we define as years 1990-2103), for New York City. Answer the following questions:

 

1. a) For how many years during the recent period, did the annual temperature rise above the

historical mean calculated for the entire period? Does this represent a reasonable, relatively

large or relatively small percentage of the recent years?

 

1. b) Of the 25 warmest years in recorded history, what percentage occurs during the recent period?

Do you think the recent period has more or less than its fair share of warmest years?

(Hint: It may help to re-sort the data according to the temperature).

 

1. c) Is the mean temperature for the recent period higher or lower than that of the entire period?

Calculate the z-score for the recent mean based on the mean and standard deviation for the

entire period. What does the value of the z-score tell you about the difference between the two

means?

 

1. d) Draw a Box plot for the recent years and place it next to the Box Plot obtained from the data

corresponding to the years prior to 1990. Are there any noteworthy differences between the

two?

 

1. e) Write a paragraph to summarize your findings: are New York city temperatures notably

different in recent times from what they were in the earlier part of the observation period. In

what way?

 

 

 

 

 

 

 

Exercise 4B

Repeat the process for Sydney

 

Extra Credit: Repeat Exercise 4 for the city of your choice.

 

Exercise 5A

1. a) Use a statistical package to find the value of the linear correlation coefficient between “year”

and “NYCtemp”.

1. b) Is the correlation significant? Explain the reason for your answer.
2. c) If the correlation is significant, what does it imply about the trend in temperatures?
3. d) Find the equation for the least square regression (LSR) line.
4. e) Interpret the meaning of the slope of the LSR line.
5. f) Based on the equation of the LSR line, what is the best “predicted” value for the NYC Annual

Average Temperature for 2013? How accurate is the prediction?

1. g) Can we use this LSR line equation to predict the Annual average Temperature for the future?

Explain.

1. h) Write a paragraph to summarize your findings: Is there statistically significant evidence of any

pattern or trend in temperature over the observation period in NYC?

 

Exercise 5B: Repeat the process for Sydney.

 

Extra Credit: Repeat Exercise 5 for the city of your choice.

 

 

Exercise 6

 

• Does your analysis of the historical temperature data for several cities, provide evidence for

the existence of the temperature increasing trend around the world? Why or why not?

 

Include a graph or char to support your claim.

 

 

• Based on your analyses, can you conclude whether the Global Warming is occurring? Why or why not?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

NEW YORK CITY TEMPERATURES

Year                            temp                            Year                            temp                            Year                            temp                            Year                            temp               

1869                            51.4                             1914                            51.1                             1959                            54.6                             2004                            74.1

1870                            53.6                             1915                            52.2                             1960                            53.1                             2005                            74.1

1871                            51.1                             1916                            51.1                             961                              53.9                             2006                            73.6

1872                            51                                            1917                            49.7                             1962                            52.4                             2007                            72.9

1873                            51                                            1918                            52.1                             1963                            52.5                             2008                            71.8

1874                            51.3                             1919                            52.8                             1964                            53.5                             2009                            73.2

1875                            49.4                             1920                            51.7                             1965                            53.1                             2010                            72.7

1876                            51.9                             1921                            54.4                             1966                            53.9                             2011                            72.7

1877                            52.8                             1922                            52.8                             1967                            51.9                             2012                            72.9

1878                            53.6                             1923                            52                                            1968                            53                                            2013                            74.4

1879                            52.3                             1924                            51.1                             1969                            53.7

1880                            53.2                             1925                            52.7                             1970                            53.2

1881                            52.4                             1926                            50.2                             1971                            54.1

1882                            52                                            1927                            52.6                             1972                            53

1883                            50.5                             1928                            52.7                             1973                            55.3

1884                            52.4                             1929                            53.2                             1974                            54.2

1885                            51.1                             1930                            53.7                             1975                            54.4

1886                            51                                            1931                            55.1                             1976                            52.8

1887                            50.9                             1932                            54.3                             1977                            53.4

1888                            49.3                             1933                            53.5                             1978                            52

1889                            52.7                             1934                            52                                            1979                            54.1

1890                            52.7                             1935                            52.3                             1980                            53.6

1891                            53.8                             1936                            52.6                             1981                            53.9

1892                            51.9                             1937                            53.5                             1982                            53.5

1893                            50.4                             1938                            54                                            1983                            54.7

1894                            52.8                             1939                            53.5                             1984                            54.1

1895                            51.3                             1940                            50.7                             1985                            54.2

1896                            51.7                             1941                            53.6                             1986                            54.2

1897                            51.6                             1942                            52.8                             1987                            54.3

1898                            53                                            1943                            52.6                             1988                            54

1899                            52                                            1944                            53.4                             1989                            53.2

1900                            52.4                             1945                            53                                            1990                            56.4

1901                            50.6                             1946                            54.2                             1991                            56.4

1902                            51.2                             1947                            52.8                             1992                            53.1

1903                            51.2                             1948                            53                                            1993                            54.7

1904                            48.7                             1949                            55.9                             1994                            54.4

1905                            51.2                             1950                            52.6                             1995                            54.4

1906                            52.7                             1951                            54                                            1996                            53.7

1907                            50.4                             1952                            54.8                             1997                            54.3

1908                            52.5                             1953                            56                                            1998                            57.1

1909                            51.4                             1954                            53.9                             1999                            56.5

1910                            51                                            1955                            53.9                             2000                            53.8

1911                            52.2                             1956                            52.7                             2001                            56.2

1912                            51.7                             1957                            54.7                             2002                            56.4

1913                            53.9                             1958                            51.8                             2003                            53.4

 

SIDNEY         TEMPERATURES

Year                            temp                            Year                            temp                            Year                            temp                            Year                            temp

1859                            70.5                             1905                            69.6                             1951                            71.2                             1997                            72.3

1860                            68.8                             1906                            70.7                             1952                            70.7                             1998                            72.9

1861                            69.6                             1907                            70.5                             1953                            71.1                             1999                            71.8

1862                            70.5                             1908                            70.3                             1954                            71.1                             2000                            72.9

1863                            69.8                             1909                            70                                            1955                            71.2                             2001                            73.6

1864                            69.1                             1910                            70.5                             1956                            70.9                             2002                            73.6

1865                            71.1                             1911                            70.3                             1957                            71.8                             2003                            72.9

1866                            70.3                             1912                            70.5                             1958                            72                                            2004                            74.1

1867                            71.2                             1913                            70.9                             1959                            71.2                             2005                            74.1

1868                            70.5                             1914                            71.6                             1960                            70.9                             2006                            73.6

1869                            70                                            1915                            71.4                             1961                            71.2                             2007                            72.9

1870                            69.3                             1916                            70                                            1962                            71.4                             2008                            71.8

1871                            69.4                             1917                            69.8                             1963                            71.1                             2009                            73.2

1872                            69.3                             1918                            71.2                             1964                            72.1                             2010                            72.7

1873                            69.6                             1919                            72.7                             1965                            71.8                             2011                            72.7

1874                            70                                            1920                            71.1                             1966                            70.9                             2012                            72.9

1875                            70.5                             1921                            72                                            1967                            71.1                             2013                            74.7

1876                            70.3                             1922                            72.5                             1968                            72.7

1877                            70.5                             1923                            72.3                             1969                            71.8

1878                            70.5                             1924                            71.2                             1970                            71.6

1879                            68.2                             1925                            70.5                             1971                            71.4

1880                            69.4                             1926                            72.5                             1972                            71.4

1881                            68.9                             1927                            70.2                             1973                            72.9

1882                            70.2                             1928                            72.3                             1974                            71.1

1883                            69.3                             1929                            70.5                             1975                            72.5

1884                            70.2                             1930                            70.5                             1976                            71.8

1885                            70.9                             1931                            70.9                             1977                            72.9

1886                            70.3                             1932                            70.7                             1978                            71.2

1887                            68.5                             1933                            69.6                             1979                            72.3

1888                            69.8                             1934                            70.3                             1980                            73.4

1889                            69.4                             1935                            71.1                             1981                            71.8

1890                            69.1                             1936                            71.1                             1982                            72

1891                            69.3                             1937                            70.9                             1983                            72

1892                            68.7                             1938                            71.8                             1984                            71.6

1893                            68.9                             1939                            71.4                             1985                            72.6

1894                            69.6                             1940                            72                                            1986                            72

1895                            69.8                             1941                            70.9                             1987                            72

1896                            69.6                             1942                            71.1                             1988                            73.2

1897                            70.7                             1943                            69.1                             1989                            71.8

1898                            70.3                             1944                            70.9                             1990                            72.1

1899                            69.8                             1945                            70.5                             1991                            73

1900                            69.6                             1946                            71.2                             1992                            70.7

1901                            69.8                             1947                            70.9                             1993                            72.1

1902                            69.8                             1948                            70.3                             1994                            72.7

1903                            69.3                             1949                            70.3                             1995                            71.2

1904                            69.6                             1950                            70.5                             1996                            71.8