Getting Started With R Part 2

Case-scenario 1 This is the fourth season of outfielder Luis Robert with the Chicago White Socks. If during the first three seasons he hit 11, 13, and 12 home runs, how many does he need on this season for his overall average to be at least 20?

# Home runs so far
HR_Before<-c(11,13,12)
Wanted_Homeruns<-20
n_seasons<-4
# 20 = (11 + 13 + 12 + x) / 4
# 80 - 26 = x
x_4<-n_seasons*Wanted_Homeruns-sum(HR_Before)
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.

We could confirm this, by using the function mean() in R

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

# Find mean
mean(Robert_HRs)

[1] 20

# Find std dev
sd(Robert_HRs)

[1] 16.02082

# Find maximum
max(Robert_HRs)

[1] 44

# Find minimum
min(Robert_HRs)

[1] 11

#We can use summary() to find basic statistics
#Or we would use fivenum() for Tukey's five, but summary() has the mean included, and the fields are labelled
summary(Robert_HRs)

   Min. 1st Qu.  Median    Mean 3rd Qu. 
  11.00   11.75   12.50   20.00   20.75 
   Max. 
  44.00 

Question 1 This is the sixth season of outfielder Juan Soto in the majors. If during the first five seasons he received 79, 108,41,145, and 135 walks, how many does he need on this season for his overall number of walks per season to be at least 100?

# walks so far
Walks_Before<-c(79,108,41,145,135)
Wanted_Walks<-100
n_seasons<-6
# 100 = (79 + 108 + 41 + 145 + 135 + x) / 6
x_6<-n_seasons*Wanted_Walks-sum(Walks_Before)
x_6

[1] 92

Juan Soto needs at least 92 walks in his 6th season in order for the mean of all 6 seasons to be 100 walks

Case-Scenario 2 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_avg<- (n_1 * y_1 + n_2 * y_2) / (n_1 + n_2)
salary_avg

[1] 75428.57

The average salary of all the players in $75,428.57

Question 2 The average salary of 7 basketball players is 102,000 dollars a week and the average salary of 9 NFL players is 91,000. Find the mean salary of all 16 professional players.

p_1<-7
s_1<-102000
p_2<-9
s_2<-91000
avg_sal<- (p_1*s_1 + p_2*s_2) / (p_1 + p_2)
avg_sal

[1] 95812.5

The average salary of all the players is $95,812.50

getwd()

[1] "/cloud/project"

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

contracts_mean<-mean(contract_years)
contracts_mean<-round(contracts_mean,digits=3)
contracts_mean

[1] 3.459

#Median
contracts_median<-median(contract_years)
contracts_median

[1] 3

#Find the number of observations
contracts_n<-length(contract_years)
#Find Standard Deviation
contracts_sd<-sd(contract_years)
contracts_sd

[1] 1.69686

contracts_w1sd<-sum((contract_years-contracts_mean)/contracts_sd<1)/contracts_n
contracts_w1sd

[1] 0.8416834

#Differenec from empirical
contracts_w1sd-0.68

[1] 0.1616834

#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

#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

Create a Histogram

hist(contract_years,xlab= "Years Left in Contract",col = "green",border = "red",xlim = c(1,6),ylim = c(0,250),breaks = 5)

NA

#Boxplot
boxplot(contract_years,main = "Years Left in Contract",ylab = "Years")

boxplot(contract_years,main = "Years Left in Contract",ylab = "Years",col = "lightblue",border = "darkblue",horizontal = FALSE)

Question 3

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

doubles_hit_mean<-mean(doubles_hit)
doubles_hit_median<-median(doubles_hit)
doubles_hit_mean

[1] 23.55

doubles_hit_median

[1] 23.5

doubles_hit_n<-length(doubles_hit)
doubles_hit_n

[1] 100

doubles_hit_sd<-sd(doubles_hit)
doubles_hit_sd

[1] 13.37371

#Percentage within 1 sd of the mean
doubles_hit_w1sd<-sum((doubles_hit-doubles_hit_mean)/doubles_hit_sd<1)/doubles_hit_n
doubles_hit_w1sd

[1] 0.79

#Difference from empirical
doubles_hit_w1sd-0.68

[1] 0.11

#Percentage within 2 sd of the mean
doubles_hit_w2sd<-sum((doubles_hit-doubles_hit_mean)/doubles_hit_sd<2)/doubles_hit_n
doubles_hit_w2sd

[1] 1

#Difference from empirical
doubles_hit_w2sd-0.95

[1] 0.05

#Percentage within 3 sd of the mean
doubles_hit_w3sd<-sum((doubles_hit-doubles_hit_mean)/doubles_hit_sd<3)/doubles_hit_n
doubles_hit_w3sd

[1] 1

#Difference from empirical
doubles_hit_w3sd-0.9973

[1] 0.0027

#Histogram
hist(doubles_hit, xlab="Number of Doubles", col="blue", border="lightblue", xlim = c(0,60), ylim = c(0,20), breaks=7)

#Boxplot
boxplot(doubles_hit,main="Boxplot of Doubles Hit by Player", ylab="Doubles", col = "lightblue", border = "black")

I prefer to have the border be a darker color than the inner color