Need help with b and c please. Exercise 4A Limit your attention to the most “recent” temperature data, (which we define as years 1990- 2013), for New York City. Answer the following questions: 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? 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 warmer years? (Hint: It may help to re-sort the data according to temperature). 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?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Need help with b and c please.
Exercise 4A
Limit your attention to the most “recent” temperature data, (which we define as years 1990-
2013), for New York City. Answer the following questions:
a) For how many years during the recent period, did the annual temperature rise above the
historical
large or relatively small percentage of the recent years?
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 warmer years?
(Hint: It may help to re-sort the data according to temperature).
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?
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?
e) Write a paragraph to summarize your findings: are NYC annual temperatures notably
different in recent times from what they were in the earlier part of the observation period. In
what way?
| Year | NYCtemp |
| 1869 | 51.4 |
| 1870 | 53.6 |
| 1871 | 51.1 |
| 1872 | 51 |
| 1873 | 51 |
| 1874 | 51.3 |
| 1875 | 49.4 |
| 1876 | 51.9 |
| 1877 | 52.8 |
| 1878 | 53.6 |
| 1879 | 52.3 |
| 1880 | 53.2 |
| 1881 | 52.4 |
| 1882 | 52 |
| 1883 | 50.5 |
| 1884 | 52.4 |
| 1885 | 51.1 |
| 1886 | 51 |
| 1887 | 50.9 |
| 1888 | 49.3 |
| 1889 | 52.7 |
| 1890 | 52.7 |
| 1891 | 53.8 |
| 1892 | 51.9 |
| 1893 | 50.4 |
| 1894 | 52.8 |
| 1895 | 51.3 |
| 1896 | 51.7 |
| 1897 | 51.6 |
| 1898 | 53 |
| 1899 | 52 |
| 1900 | 52.4 |
| 1901 | 50.6 |
| 1902 | 51.2 |
| 1903 | 51.2 |
| 1904 | 48.7 |
| 1905 | 51.2 |
| 1906 | 52.7 |
| 1907 | 50.4 |
| 1908 | 52.5 |
| 1909 | 51.4 |
| 1910 | 51 |
| 1911 | 52.2 |
| 1912 | 51.7 |
| 1913 | 53.9 |
| 1914 | 51.1 |
| 1915 | 52.5 |
| 1916 | 51.1 |
| 1917 | 49.7 |
| 1918 | 52.1 |
| 1919 | 52.8 |
| 1920 | 51.7 |
| 1921 | 54.4 |
| 1922 | 52.8 |
| 1923 | 52 |
| 1924 | 51.1 |
| 1925 | 52.7 |
| 1926 | 50.2 |
| 1927 | 52.6 |
| 1928 | 52.7 |
| 1929 | 53.2 |
| 1930 | 53.7 |
| 1931 | 55.1 |
| 1932 | 54.3 |
| 1933 | 53.5 |
| 1934 | 52 |
| 1935 | 52.3 |
| 1936 | 52.6 |
| 1937 | 53.5 |
| 1938 | 54 |
| 1939 | 53.5 |
| 1940 | 50.7 |
| 1941 | 53.6 |
| 1942 | 52.8 |
| 1943 | 52.6 |
| 1944 | 53.4 |
| 1945 | 53 |
| 1946 | 54.2 |
| 1947 | 52.8 |
| 1948 | 53 |
| 1949 | 55.9 |
| 1950 | 52.6 |
| 1951 | 54 |
| 1952 | 54.8 |
| 1953 | 56 |
| 1954 | 53.9 |
| 1955 | 53.9 |
| 1956 | 52.7 |
| 1957 | 54.7 |
| 1958 | 51.8 |
| 1959 | 54.6 |
| 1960 | 53.1 |
| 1961 | 53.9 |
| 1962 | 52.4 |
| 1963 | 52.5 |
| 1964 | 53.5 |
| 1965 | 53.1 |
| 1966 | 53.9 |
| 1967 | 51.9 |
| 1968 | 53 |
| 1969 | 53.7 |
| 1970 | 53.2 |
| 1971 | 54.1 |
| 1972 | 53 |
| 1973 | 55.3 |
| 1974 | 54.2 |
| 1975 | 54.4 |
| 1976 | 52.8 |
| 1977 | 53.4 |
| 1978 | 52 |
| 1979 | 54.1 |
| 1980 | 53.6 |
| 1981 | 53.9 |
| 1982 | 53.5 |
| 1983 | 54.7 |
| 1984 | 54.1 |
| 1985 | 54.2 |
| 1986 | 54.2 |
| 1987 | 54.3 |
| 1988 | 54 |
| 1989 | 53.2 |
| 1990 | 56.4 |
| 1991 | 56.4 |
| 1992 | 53.1 |
| 1993 | 54.7 |
| 1994 | 54.4 |
| 1995 | 54.4 |
| 1996 | 53.7 |
| 1997 | 54.3 |
| 1998 | 57.1 |
| 1999 | 56.5 |
| 2000 | 53.8 |
| 2001 | 56.2 |
| 2002 | 56.4 |
| 2003 | 53.4 |
| 2004 | 54.5 |
| 2005 | 55.7 |
| 2006 | 56.8 |
| 2007 | 55 |
| 2008 | 55.3 |
| 2009 | 54 |
| 2010 | 56.7 |
| 2011 | 56.4 |
| 2012 | 57.3 |
| 2013 | 55.5 |
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