Exam 2

Question 5

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

fg_percent <- made / attempted
mean(fg_percent)

[1] 0.4686539

sum(made) / sum(attempted)

[1] 0.4666667

Total Made = 18 + 7 + 6 + 9 + 10 + 13 = 63 Total Attempted = 36 + 23 + 12 + 18 + 24 + 22 = 135 63/135= 0.4667

Quetion 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 and attempted in seven games
three_made <- c(3, 5, 10, 6, 3, 7, 1)
three_attempted <- c(9, 10, 18, 12, 11, 12, 11)

# Individual three-point percentage for each game
game_pct <- three_made / three_attempted
game_pct

[1] 0.33333333 0.50000000 0.55555556 0.50000000 0.27272727 0.58333333 0.09090909

# Average of the seven individual game percentages
average_game_pct <- mean(game_pct)
average_game_pct

[1] 0.4051227

# Overall cumulative three-point percentage
overall_pct <- sum(three_made) / sum(three_attempted)
overall_pct

[1] 0.4216867

# Display both results as percentages
average_game_pct * 100

[1] 40.51227

overall_pct * 100

[1] 42.16867

mean(three_made / three_attempted)

[1] 0.4051227

Individual per-game three-point percentages = 0.4051 * 100 = 40.51%

Overall cumulative percentage 42.16867 around up 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))

# Create the data
PlayerID = c(1,2,3,4,5)
Hits = c(112,124,121,106,140)
AtBats = c(400,450,380,500,402)
BB = c(50,60,19,150,55)

# Create data frame
baseball = data.frame(PlayerID, Hits, AtBats, BB)

# Calculate OBP
baseball$OBP = (baseball$Hits + baseball$BB) /
               (baseball$AtBats + baseball$BB)

# Display the data
baseball

Player 5 had the highest OBP at 0.4267, meaning this player reached base more frequently than the other players.