a. See below for the Frequency and Relative frequency Table.
b. Pitcher (P) is the position provides the most Hall of Famers.
c. 3rd base (3) is the position that provides the fewest Hall of Famers.
d. R is the outfield position that provides the most Hall of Famers.
e. Th number of Hall of Famers of Infielders which is 16 is less than the 18 Hall of Famers of those of outfielders.
Step-by-step explanation:
Note: This question not complete. The complete question is therefore provided before answering the question as follows:
Data for a sample of 55 members of the Baseball Hall of Fame in Cooperstown, New York, are shown here. Each observation indicates the primary position played by the Hall of Famers: pitcher (P), catcher (H), 1st base (1), 2nd base (2), 3rd base (3), shortstop (S), left field (L), center field (C), and right field (R).
L P C H 2 P R 1 S S 1 L P R P
P P P R C S L R P C C P P R P
2 3 P H L P 1 C P P P S 1 L R
R 1 2 H S 3 H 2 L P
a. Use frequency and relative frequency distributions to summarize the data.
b. What position provides the most Hall of Famers?
c. What position provides the fewest Hall of Famers?
d. What outfield position (L, C, or R) provides the most Hall of Famers?
e. Compare infielders (1, 2, 3, and S) to outfielders (L, C, and R).
The explanation of the answers is now provided as follows:
a. Use frequency and relative frequency distributions to summarize the data.
The frequency is the number of times a position occurs in the sample, while the relative frequency is calculated as the frequency of each position divided by the sample size multiplied by 100.
Therefore, we have:
Frequency and Relative frequency Table Â
Position      Frequency      Relative frequency (%)
P Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 17 Â Â Â Â Â Â Â Â Â Â Â Â Â Â 30.91%
H Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 4 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 7.27%
1 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 5 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 9.09%
2 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 4 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 7.27%
3 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 2 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 3.64%
S Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 5 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 9.09%
L Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 6 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 10.91%
C Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 5 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 9.09%
R Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 7 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 12.73%
Total            55                100% Â
b. What position provides the most Hall of Famers?
As it can be seen from the frequency table in part a, Pitcher (P) has the highest frequency which is 17. Therefore, Pitcher (P) is the position provides the most Hall of Famers.
c. What position provides the fewest Hall of Famers?
As it can be seen from the frequency table in part a, 3rd base (3) has the lowest frequency which is 2. Therefore, 3rd base (3) is the position that provides the fewest Hall of Famers.
d. What outfield position (L, C, or R) provides the most Hall of Famers?
As it can be seen from the frequency table in part a, we have:
Frequency of L = 6
Frequency of C = 5
Frequency of R = 7
Since R has the highest frequency which is 7 among the outfield position (L, C, or R), it implies that R is the outfield position that provides the most Hall of Famers.
e. Compare infielders (1, 2, 3, and S) to outfielders (L, C, and R).
Total frequency of infielders = Frequency of 1 + Frequency of 2 + Frequency of 3 + Frequency of S = 5 + 4 + 2 + 5 = 16
Total frequency of outfielders = Frequency of L + Frequency of C + Frequency of R = 6 + 5 + 7 = 18
The calculated total frequencies above imply that number of Hall of Famers of Infielders which is 16 is less than the 18 Hall of Famers of those of outfielders.
