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.

Question states Five Games but there’s data for Six Games

field_goals_made = c(18,7,6,9,10,13)
field_goals_attempted = c(36,23,12,18,24,22)
fg_percentage <- (field_goals_made / field_goals_attempted) * 100
field_goals_made

[1] 18  7  6  9 10 13

field_goals_attempted

[1] 36 23 12 18 24 22

round(fg_percentage,2)

[1] 50.00 30.43 50.00 50.00 41.67 59.09

total_avg_fg_percentage <- mean(fg_percentage)
round(total_avg_fg_percentage,2)

[1] 46.87

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.

Three_Pointers_Made <- c(3,5,10,6,3,7,1)
Three_Pointers_Attempted <- c(9,10,18,12,11,12,11)
threepoint_percentage <- (Three_Pointers_Made/Three_Pointers_Attempted)*100
Three_Pointers_Made

[1]  3  5 10  6  3  7  1

Three_Pointers_Attempted

[1]  9 10 18 12 11 12 11

round(threepoint_percentage,2)

[1] 33.33 50.00 55.56 50.00 27.27 58.33  9.09

overall_threepoint_percentage <- (sum(Three_Pointers_Made)/sum(Three_Pointers_Attempted))*100
round(overall_threepoint_percentage,2)

[1] 42.17

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).

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

Compute the On-Base Percentage (OBP) for each player and select the player with the highest OBP.

(Formula: OBP = (Hits + Walks) / (At-Bats + Walks))

players <- data.frame(
  PlayerID = c(1,2,3,4,5),
  Hits = c(112, 124,121,106,140),
  At_Bats = 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)
)

players$OBP <- (players$Hits+players$BB)/(players$At_Bats+players$BB)
players$OBP <- round(players$OBP,3)
players

According to our Dataset the player with the highest OBP will be Player 5 with an OBP of 0.427