Final Exam

# Question 1:
# Calculate the field goal percentage for each game and the average field goal percentage 
# given the following vectors:
# Field Goals Made: (18, 7, 6, 9, 10, 13)
# Field Goals Attempted: (36, 23, 12, 18, 24, 22)

# Data
field_goals_made <- c(18, 7, 6, 9, 10, 13)
field_goals_attempted <- c(36, 23, 12, 18, 24, 22)

# Field goal percentage per game
field_goal_percentage <- (field_goals_made / field_goals_attempted) * 100
field_goal_percentage

[1] 50.00000 30.43478 50.00000 50.00000 41.66667
[6] 59.09091

# Average field goal percentage
average_field_goal_percentage <- mean(field_goal_percentage)
average_field_goal_percentage

[1] 46.86539

The field goal percentages for each game were approximately 50.00%, 30.43%, 50.00%, 50.00%, 41.67%, and 59.09%. The average field goal percentage across all games is approximately 46.87%.

# Question 2:
# Calculate the three-point shooting percentage for each game and the average three-point shooting percentage 
# given the following vectors:
# Three-Pointers Made: (3, 5, 0, 6, 3, 7)
# Three-Pointers Attempted: (9, 10, 8, 12, 11, 12)

# Data
three_pointers_made <- c(3, 5, 0, 6, 3, 7)
three_pointers_attempted <- c(9, 10, 8, 12, 11, 12)

# Three-point shooting percentage per game
three_point_percentage <- (three_pointers_made / three_pointers_attempted) * 100
three_point_percentage

[1] 33.33333 50.00000  0.00000 50.00000 27.27273
[6] 58.33333

# Average three-point shooting percentage
average_three_point_percentage <- mean(three_point_percentage)
average_three_point_percentage

[1] 36.4899

The player’s three-point shooting percentages for each game were approximately 33.33%, 50.00%, 0.00%, 50.00%, 27.27%, and 58.33%. The average three-point shooting percentage across all games is approximately 36.49%.

# Question 3:
# Compute the On-Base Percentage (OBP) for each player and select the player with the highest OBP.
# Given data:
# PlayerID     Hits    At-Bats   HR   BB   SO
# 1            112     400       25   50   60
# 2            124     450       22   60   65
# 3            121     380        8   19   67
# 4            106     500       20  150   92
# 5            140     402       11   55   70
# Formula: OBP = (Hits + Walks) / (At-Bats + Walks)

# Data
hits <- c(112, 124, 121, 106, 140)
at_bats <- c(400, 450, 380, 500, 402)
walks <- c(50, 60, 19, 150, 55)

# Calculate OBP for each player
obp <- (hits + walks) / (at_bats + walks)
obp

[1] 0.3600000 0.3607843 0.3508772 0.3938462
[5] 0.4266958

# Find the player with the highest OBP
highest_obp_player <- which.max(obp)
highest_obp_player

[1] 5

The On-Base Percentages (OBP) for the players are approximately:

Player 1: 36.00%

Player 2: 36.08%

Player 3: 35.09%

Player 4: 39.38%

Player 5: 42.67%

The player with the highest OBP is Player 5.