Assignment5

# Walks in the first 5 seasons
walks_before <- c(79, 108, 41, 145, 135)

# Desired average
wanted_walks <- 100

# Number of seasons
n_seasons <- 6

# Needed walks in season 6
x_6 <- n_seasons * wanted_walks - sum(walks_before)
x_6

[1] 92

# Full walk performance including needed 6th season value
Soto_walks <- c(walks_before, x_6)

# Mean
mean(Soto_walks)

[1] 100

# Standard deviation
sd(Soto_walks)

[1] 38.20995

# Max
max(Soto_walks)

[1] 145

# Min
min(Soto_walks)

[1] 41

# Summary
summary(Soto_walks)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  41.00   82.25  100.00  100.00  128.25  145.00 

# Number of players
n_basketball <- 7
n_nfl <- 9

# Average salaries
avg_basketball <- 102000
avg_nfl <- 91000

# Combined mean salary
combined_salary <- (n_basketball * avg_basketball + n_nfl * avg_nfl) / (n_basketball + n_nfl)
combined_salary

[1] 95812.5

# Load CSV file with contract years
contract_length <- read.csv(("/Users/sarahguzman/Desktop/SPECIAL_TOPICS_SPORTS/allcontracts.csv"), header = TRUE)
contract_years <- contract_length$years

# Mean contract length
contracts_mean <- mean(contract_years)
contracts_mean

[1] 3.458918

# Median contract length
contracts_median <- median(contract_years)
contracts_median

[1] 3

# Number of observations
contracts_n <- length(contract_years)

# Standard deviation
contracts_sd <- sd(contract_years)
contracts_sd

[1] 1.69686

# Within 1 SD
contracts_w1sd <- sum(abs(contract_years - contracts_mean) < contracts_sd) / contracts_n
contracts_w1sd

[1] 0.6693387

contracts_w1sd - 0.68  # Compare to empirical rule

[1] -0.01066132

# Within 2 SD
contracts_w2sd <- sum(abs(contract_years - contracts_mean) < 2 * contracts_sd) / contracts_n
contracts_w2sd

[1] 1

contracts_w2sd - 0.95

[1] 0.05

# Within 3 SD
contracts_w3sd <- sum(abs(contract_years - contracts_mean) < 3 * contracts_sd) / contracts_n
contracts_w3sd

[1] 1

contracts_w3sd - 0.9973

[1] 0.0027

hist(contract_years,
     xlab = "Years Left in Contract",
     col = "green",
     border = "red",
     xlim = c(0, 8),
     ylim = c(0, 225),
     breaks = 5,
     main = "Distribution of Contract Lengths")