Ted Williams played for the Boston Red Sox from 1939-1960. Many people credit him with being the greatest hitter of all time. Unfortunately, his career totals are somewhat less impressive than others because his career was interrupted from 1943-1945 by World War II and from 1952-1953 by the Korean War. Some assert that if he had been playing during the war years, he would have broken Hank Aaron’s home run record of 755 and runs batted in (RBI) record of 2297. Below are Williams’ statistics. Year Number of home runs Number of RBIs 1939 31 145 1940 23 113 1941 37
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.
Ted Williams played for the Boston Red Sox from 1939-1960. Many people credit him with being the greatest hitter of all time. Unfortunately, his career totals are somewhat less impressive than others because his career was interrupted from 1943-1945 by World War II and from 1952-1953 by the Korean War. Some assert that if he had been playing during the war years, he would have broken Hank Aaron’s home run record of 755 and runs batted in (RBI) record of 2297. Below are Williams’ statistics.
|
Year |
Number of home runs |
Number of RBIs |
|
1939 |
31 |
145 |
|
1940 |
23 |
113 |
|
1941 |
37 |
120 |
|
1942 |
36 |
137 |
|
1943 |
0* |
0* |
|
1944 |
0* |
0* |
|
1945 |
0* |
0* |
|
1946 |
38 |
123 |
|
1947 |
32 |
114 |
|
1948 |
25 |
127 |
|
1949 |
43 |
159 |
|
1950 |
28 |
97 |
|
1951 |
30 |
126 |
|
1952 |
1* |
3* |
|
1953 |
13* |
34* |
|
1954 |
29 |
89 |
|
1955 |
28 |
83 |
|
1956 |
24 |
82 |
|
1957 |
38 |
87 |
|
1958 |
26 |
85 |
|
1959 |
10 |
43 |
|
1960 |
29 |
72 |
a.Excluding the data for the war years (indicated by *) find a linear regression equation for RBIs.
b.What is the coefficient of determination? What does it
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