Question

The Boys of Summer

Which baseball league has had the best hitters? Many of us have heard of baseball greats like Stan Musial, Hank Aaron, Roberto Clemente, and Pete Rose of the National League and Ty Cobb, Babe Ruth, Ted Williams, Rod Carew, and Wade Boggs of the American League. But have you ever heard of Willie Keeler, who batted .432 for the Baltimore Orioles, or Nap Lajoie, who batted .422 for the Philadelphia A’s? The batting averages for the batting champions of the National and American Leagues are given on the CourseMate Web site.

The batting averages for the National League begin in 1876 with Roscoe Barnes, whose batting average was .403 when he played with the Chicago Cubs. The last entry for the National League is for the year 2010, when Carlos Gonzalez of the Colorado Rockies averaged .336. The American League records begin in 1901 with Nap Lajoie of the Philadelphia A’s, who batted .422, and end in 2010 with Josh Hamilton of the Texas Rangers, who batted .359. How can we summarize the information in this data set?

Questions to be answered in your report –

1. Use MS Excel, MINITAB, or another statistical software package to describe the bat- ting averages for the American and National League batting champions. Generate any graphics that may help you in interpreting these data sets.
2. Does one league appear to have a higher percentage of hits than the other? Do the batting averages of one league appear to be more variable than the other?
3. Are there any outliers in either league?
4. Summarize your comparison of the two baseball leagues.

LEAGUE	YEAR	AVERAGE
0	1876	0.403
0	1877	0.385
0	1878	0.356
0	1879	0.407
0	1880	0.365
0	1881	0.399
0	1882	0.367
0	1883	0.371
0	1884	0.35
0	1885	0.371
0	1886	0.388
0	1887	0.421
0	1888	0.343
0	1889	0.373
0	1890	0.336
0	1891	0.338
0	1892	0.335
0	1893	0.378
0	1894	0.438
0	1895	0.423
0	1896	0.41
0	1897	0.432
0	1898	0.379
0	1899	0.408
0	1900	0.38
0	1901	0.382
0	1902	0.357
0	1903	0.355
0	1904	0.349
0	1905	0.377
0	1906	0.339
0	1907	0.35
0	1908	0.354
0	1909	0.339
0	1910	0.331
0	1911	0.334
0	1912	0.372
0	1913	0.35
0	1914	0.329
0	1915	0.32
0	1916	0.339
0	1917	0.341
0	1918	0.335
0	1919	0.321
0	1920	0.37
0	1921	0.397
0	1922	0.401
0	1923	0.384
0	1924	0.424
0	1925	0.403
0	1926	0.353
0	1927	0.38
0	1928	0.387
0	1929	0.398
0	1930	0.401
0	1931	0.349
0	1932	0.368
0	1933	0.368
0	1934	0.362
0	1935	0.385
0	1936	0.373
0	1937	0.374
0	1938	0.342
0	1939	0.349
0	1940	0.355
0	1941	0.343
0	1942	0.33
0	1943	0.357
0	1944	0.357
0	1945	0.355
0	1946	0.365
0	1947	0.363
0	1948	0.376
0	1949	0.342
0	1950	0.346
0	1951	0.355
0	1952	0.336
0	1953	0.344
0	1954	0.345
0	1955	0.338
0	1956	0.328
0	1957	0.351
0	1958	0.35
0	1959	0.355
0	1960	0.325
0	1961	0.351
0	1962	0.346
0	1963	0.326
0	1964	0.339
0	1965	0.329
0	1966	0.342
0	1967	0.357
0	1968	0.335
0	1969	0.348
0	1970	0.366
0	1971	0.363
0	1972	0.333
0	1973	0.338
0	1974	0.353
0	1975	0.354
0	1976	0.339
0	1977	0.338
0	1978	0.334
0	1979	0.344
0	1980	0.324
0	1981	0.341
0	1982	0.331
0	1983	0.323
0	1984	0.351
0	1985	0.353
0	1986	0.334
0	1987	0.37
0	1988	0.313
0	1989	0.336
0	1990	0.335
0	1991	0.319
0	1992	0.33
0	1993	0.37
0	1994	0.394
0	1995	0.368
0	1996	0.353
0	1997	0.372
0	1998	0.363
0	1999	0.379
0	2000	0.372
0	2001	0.35
0	2002	0.37
0	2003	0.359
0	2004	0.362
0	2005	0.335
0	2006	0.344
1	1901	0.422
1	1902	0.376
1	1903	0.355
1	1904	0.381
1	1905	0.306
1	1906	0.358
1	1907	0.35
1	1908	0.324
1	1909	0.377
1	1910	0.385
1	1911	0.42
1	1912	0.41
1	1913	0.39
1	1914	0.368
1	1915	0.37
1	1916	0.386
1	1917	0.383
1	1918	0.382
1	1919	0.407
1	1920	0.407
1	1921	0.394
1	1922	0.42
1	1923	0.403
1	1924	0.378
1	1925	0.393
1	1926	0.377
1	1927	0.398
1	1928	0.379
1	1929	0.369
1	1930	0.381
1	1931	0.39
1	1932	0.367
1	1933	0.356
1	1934	0.363
1	1935	0.349
1	1936	0.388
1	1937	0.371
1	1938	0.349
1	1939	0.381
1	1940	0.352
1	1941	0.406
1	1942	0.356
1	1943	0.328
1	1944	0.327
1	1945	0.309
1	1946	0.352
1	1947	0.343
1	1948	0.369
1	1949	0.343
1	1950	0.354
1	1951	0.344
1	1952	0.327
1	1953	0.337
1	1954	0.341
1	1955	0.34
1	1956	0.353
1	1957	0.388
1	1958	0.328
1	1959	0.353
1	1960	0.32
1	1961	0.361
1	1962	0.326
1	1963	0.321
1	1964	0.323
1	1965	0.321
1	1966	0.316
1	1967	0.326
1	1968	0.301
1	1969	0.332
1	1970	0.329
1	1971	0.337
1	1972	0.318
1	1973	0.35
1	1974	0.364
1	1975	0.359
1	1976	0.333
1	1977	0.388
1	1978	0.333
1	1979	0.333
1	1980	0.39
1	1981	0.336
1	1982	0.332
1	1983	0.361
1	1984	0.343
1	1985	0.368
1	1986	0.357
1	1987	0.363
1	1988	0.366
1	1989	0.339
1	1990	0.329
1	1991	0.341
1	1992	0.343
1	1993	0.363
1	1994	0.359
1	1995	0.356
1	1996	0.358
1	1997	0.347
1	1998	0.339
1	1999	0.357
1	2000	0.372
1	2001	0.35
1	2002	0.349
1	2003	0.326
1	2004	0.372
1	2005	0.331
1	2006	0.347

Answer 1

a) The mean and std deviation of the batting averages of the 2 leagues are:

	League 0	League 1
Mean	0.3588	0.3575
Std Dev.	0.0257	0.0270

The means are nearly the same, though the batting average for League 0 is slightly higher than that of League 1

2) League 0 does appear to have a higher percentage of hits than League 1. Also, from the std deviations given in the table above, batting averages of League 1 appear to be more variable given its higher std deviation of 0027 (versus 0.0257 for League 0).

3) The points 0.422 in 1901 and 0.306 in 1905 for League 1 appear to be outliers.

4) League 0 has historically produced higher batting averages, with lower spread, while League 1 has produced batting averages with higher variability. However, the batting averages for both the leagues has in general been coming down over years, which one can see from the downward trending data points from left to right.