Intro to R Part 2

#Home-runs so far
HR_before <- c(11, 13, 12)
#Average Number of Home-runs per season wanted
wanted_HR <- 20
#Number of seasons
n_seasons <- 4
#Needed Home-runs on season 4
x_4 <- n_seasons*wanted_HR - sum(HR_before)
#Minimum number of Home-runs needed by Robert
x_4

[1] 44

According to the calculations above, Robert must hit 44 home-runs or better on this season to get an average number of home-runs per season of at least 20.

#Robert's performance
Robert_HRs <- c(11, 13, 12,44)
#Find mean
mean(Robert_HRs)

[1] 20

#Robert's actual performace
Robert_HR <- c(11, 13, 12,38)
mean(Robert_HR)

[1] 18.5

#Find standard deviation
sd(Robert_HR)

[1] 13.02562

#Find the maximum number of home-runs during the four seasons period
max(Robert_HR)

[1] 38

#Find the minimum number of home-runs during the four seasons period
min(Robert_HR)

[1] 11

summary(Robert_HR)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  11.00   11.75   12.50   18.50   19.25   38.00 

#Question 1
#Walks so far
walks_before <- c(79, 108, 41, 145, 135)
#Average Number of Walks per season wanted
wanted_walks <- 100
#Number of seasons
n_seasons <- 6
#Needed Walks on season 6
w_6 <- n_seasons*wanted_walks - sum(walks_before)
#Minimum number of Home-runs needed by Robert
w_6

[1] 92

#Juan Soto performance
Juan_walks <- c(79, 108, 41, 145, 135, 92)
#Find mean
mean(Juan_walks)

[1] 100

#The average salary of 10 baseball players is 72,000 dollars a week and the average salary of 4 soccer players is 84,000. Find the mean salary of all 14 professional players.

n_1 <- 10
n_2 <- 4
y_1 <- 72000
y_2 <- 84000
# Mean salary overall
salary_ave <-  (n_1*y_1 + n_2*y_2)/(n_1+n_2)
salary_ave

[1] 75428.57

n_1 <- 7
n_2 <- 9
y_1 <- 102000
y_2 <- 91000
#mean salary overall
salary_ave <- (n_1*y_1+n_2*y_2)/(n_1+n_2)
salary_ave

[1] 95812.5

getwd()

[1] "/cloud/project"

contract_length <- read.table("allcontracts.csv", header = TRUE, sep = ",")
contract_years <- contract_length$years

# 1. To find the mean and the standard deviation
#Mean 
contracts_mean  <- mean(contract_years)
contracts_mean

[1] 3.458918

#Median
contracts_median <- median(contract_years)
contracts_median

[1] 3

#Find number of observations
contracts_n <- length(contract_years)
#Find standard deviation
contracts_sd <- sd(contract_years)

# 2. What percentage of the data lies within one standard deviation of the mean?
contracts_w1sd <- sum((contract_years - contracts_mean)/contracts_sd < 1)/ contracts_n
#Percentage of observation within one standard deviation of the mean
contracts_w1sd

[1] 0.8416834

## Difference from empirical 
contracts_w1sd - 0.68

[1] 0.1616834

# 3. What percentage of the data lies within two standard deviations of the mean?
## Within 2 sd
contracts_w2sd <- sum((contract_years - contracts_mean)/ contracts_sd < 2)/contracts_n
contracts_w2sd

[1] 1

## Difference from empirical 
contracts_w2sd - 0.95

[1] 0.05

# 4. What percent of the data lies within three standard deviations of the mean?

## Within 3 sd 
contracts_w3sd <- sum((contract_years - contracts_mean)/ contracts_sd < 3)/contracts_n
contracts_w3sd

[1] 1

## Difference from empirical 
contracts_w3sd - 0.9973

[1] 0.0027

# 5. Draw a histogram
# Create histogram
hist(contract_years,xlab = "Years Left in Contract",col = "green",border = "red", xlim = c(0,6), ylim = c(0,250),
   breaks = 3)

Answers to Question 3

doubles <- read.table("doubles_hit.csv", header = TRUE, sep = ",")
doublesnumber <- doubles$doubles_hit

# Mean 
doublesnumber_mean  <- mean(doublesnumber)
doublesnumber_mean

[1] 23.55

#Median
doublesnumber_median <- median(doublesnumber)
doublesnumber_median

[1] 23.5

#Find number of observations
players_n <- length(doublesnumber)
#Find standard deviation
players_sd <- sd(doublesnumber)

# 2. What percentage of the data lies within one standard deviation of the mean?

doublesnumber_w1sd <- sum((doublesnumber - doublesnumber_mean)/players_sd < 1)/ players_n
#Percentage of observation within one standard deviation of the mean
doublesnumber_w1sd

[1] 0.79

## Difference from empirical 
doublesnumber_w1sd - 0.68

[1] 0.11

# 3. What percentage of the data lies within two standard deviations of the mean?

## Within 2 sd
doublesnumber_w2sd <- sum((doublesnumber - doublesnumber_mean)/ players_sd < 2)/players_n
doublesnumber_w2sd

[1] 1

## Difference from empirical 
doublesnumber_w2sd - 0.95

[1] 0.05

# 4. What percent of the data lies within three standard deviations of the mean?

## Within 3 sd 
doublesnumber_w3sd <- sum((doublesnumber - doublesnumber_mean)/ players_sd < 3)/players_n
doublesnumber_w3sd

[1] 1

## Difference from empirical 
doublesnumber_w3sd - 0.9973

[1] 0.0027

# 5. Draw a histogram

hist(doublesnumber,xlab = "Number of Doubles",col = "green",border = "red", xlim = c(0,60), ylim = c(0,50), breaks = 7)

According to the Histogram players hit between 10-30 doubles per Season

xlim = c(0,60), ylim = c(0,50), breaks = 7), I think this is the sweet spot to make the Histogram show exactly what we are looking for