Exam 2

#Question #5 Consider the following vectors representing the number of field goals made and attempted by a basketball player in five games:

Field Goals Made: c(18, 7, 6, 9, 10,13) Field Goals Attempted: c(36, 23, 12, 18, 24,22)

Calculate the field goal percentage for each game and select the correct average field goal percentage for the five games.

made <- c(18, 7, 6, 9, 10, 13)
attempted <- c(36, 23, 12, 18, 24, 22)

fg_pct <- made / attempted *100
mean(fg_pct)

[1] 46.86539

avg_fg_pct <- mean(fg_pct)
avg_fg_pct 

[1] 46.86539

#Question 6 Consider the following vectors in R representing the number of three-pointers made (3PM) and attempted (3PA) by a basketball player over a seven-game span:

Three-Pointers Made: c(3, 5, 10, 6, 3, 7, 1)

Three-Pointers Attempted: c(9, 10, 18, 12, 11, 12, 11)

Calculate both the average of the individual per-game three-point percentages and the overall (cumulative) three-point shooting percentage across all seven games.

made <- c(3, 5, 10, 6, 3, 7, 1)
attempted <- c(9, 10, 18, 12, 11, 12, 11)

three_pct <- (made / attempted) * 100
three_pct

[1] 33.333333 50.000000 55.555556 50.000000
[5] 27.272727 58.333333  9.090909

avg_three_pct <- mean(three_pct)
avg_three_pct

[1] 40.51227

overall_three_pct <- sum(made) / sum(attempted) * 100
overall_three_pct

[1] 42.16867

#Question 7 Consider the following dataset representing the performance of baseball players in a season. It includes the following variables: PlayerID, Hits, At-Bats, Home Runs (HR), Walks (BB), and Strikeouts (SO). Compute the On-Base Percentage (OBP) for each player and select the player with the highest OBP. (Formula: OBP = (Hits + Walks) / (At-Bats + Walks))

PlayerID <- c(1, 2, 3, 4, 5)
Hits <- c(112, 124, 121, 106, 140)
AtBats <- c(400, 450, 380, 500, 402)
HR <- c(25, 22, 8, 20, 11)
BB <- c(50, 60, 19, 150, 55)
SO <- c(60, 65, 67, 92, 70)

OBP <- (Hits + BB) / (AtBats + BB)
OBP

[1] 0.3600000 0.3607843 0.3508772 0.3938462
[5] 0.4266958

best_player <- PlayerID[which.max(OBP)]
best_player

[1] 5