134 Chapter 3 Numerical Summaries of Data Figures 3.12–3.14 illustrate the way in which boxplots reflect skewness and symmetry. 0 1 2 3 4 5 6 7 8 9 10 80 60 40 20 0 Frequency 0 1 2 3 4 5 6 7 8 9 10 Figure 3.12 Skewed to the right 10 15 20 25 30 35 40 45 50 55 60 25 20 15 10 5 0 Frequency 10 20 30 40 50 60 Figure 3.13 Skewed to the left 12 14 16 18 20 22 24 26 28 60 50 40 30 20 10 0 Frequency 12 14 16 18 20 22 24 26 28 Figure 3.14 Approximately symmetric Comparative boxplots Boxplots do not provide as much detail as histograms do regarding the shape of a data set. However, they provide an excellent method for comparing data sets. We can plot two or more boxplots, one above another, to provide an easy visual comparison. As an example, Table 3.13 presents the rainfall in Los Angeles each February for the years 1923–1964. We would like to compare these data with the February rainfall for the years 1965–2006, which was presented in Table 3.9. Table 3.13 Annual Rainfall in Los Angeles During February: 1923---1964 Year Rainfall Year Rainfall Year Rainfall Year Rainfall 1923 0.75 1934 2.04 1945 3.34 1956 0.59 1924 0.03 1935 2.23 1946 1.52 1957 1.47 1925 0.53 1936 7.25 1947 0.86 1958 6.46 1926 2.70 1937 7.87 1948 1.29 1959 3.32 1927 9.03 1938 9.81 1949 1.41 1960 2.26 1928 1.43 1939 1.13 1950 1.67 1961 0.15 1929 2.15 1940 5.43 1951 1.48 1962 11.57 1930 0.45 1941 12.42 1952 0.63 1963 2.88 1931 3.25 1942 1.05 1953 0.33 1964 0.00 1932 5.33 1943 3.07 1954 2.98 1933 0.00 1944 8.65 1955 0.68 Figure 3.15 presents comparative boxplots for February rainfall during the years 1923–1964 and 1965–2006. 0 2 4 6 8 10 12 14 1965−2006 1923−1964 Figure 3.15 Comparative boxplots for February rainfall in Los Angeles, 1923–1964 and 1965–2006 We can see that both the box and the upper whisker for 1965–2006 extend farther to the right than the corresponding elements for 1923–1964. This tells us that 1965–2006 was, on the whole, rainier than 1923–1964.We can also see that both the box and upper whisker
navidi_monk_essential_statistics_1e_ch1_3
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