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.

avg_goals <- round(Field_Goals_Made/Field_Goals_Attempted, 3)
avg_goals

[1] 0.500 0.304 0.500 0.500 0.417 0.591

mean_avg <- round(mean(avg_goals), 2)
mean_avg

[1] 0.47

avg_goals <- round(sum(Field_Goals_Made)/sum(Field_Goals_Attempted),3)
avg_goals

[1] 0.467

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.

avg_pointers <- round(Three_Pointers_Made/ Three_Pointers_Attempted, 3)
avg_pointers

[1] 0.333 0.500 0.556 0.500 0.273 0.583 0.091

#individual per game three-point percentages
round(mean(avg_pointers), 2)

[1] 0.41

#cumulative three point shooting percentage
round(sum(Three_Pointers_Made)/ sum(Three_Pointers_Attempted), 3)

[1] 0.422

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).

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)

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

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

OBP <- round((hits + BB)/(at_bats + BB),3)
OBP

[1] 0.360 0.361 0.351 0.394 0.427

The highest OBP value comes from player 5