Exercise 1: Hands on R
Thomas Rusch
July 17, 2017
This exercise lets you try a couple of data manipulation functions with R.
- In R, assign the value of 15 to a variable . Define a new vector with values {1, 2, 3, 10, 100}. Multiply the two vectors and store the result in . Look at to see how the multiplication worked. Then calculate the sum of all elements in . Now define to be a sequence from 0 to 1 with 5 equally spaced out values (so all values lie in \([0;1]\) and two consecutive values differ by the same amount). Now multiply and again and store this in . How did the multiplication behave this time? Check whether is of the same length as . Set up a matrix with the first column being and the second column being .
x<-15
y<- c(1,2,3,10,100)
z<-x*y
z## [1] 15 30 45 150 1500sum(z)## [1] 1740x<-seq(0,1,length.out=5)
x## [1] 0.00 0.25 0.50 0.75 1.00k<-x*y
k## [1] 0.0 0.5 1.5 7.5 100.0all.equal(length(k),length(z))## [1] TRUEX<-cbind(z,k)
X## z k
## [1,] 15 0.0
## [2,] 30 0.5
## [3,] 45 1.5
## [4,] 150 7.5
## [5,] 1500 100.0- Take the first column of , call this and replace the third value in with 10. Using
which(), check which elements in are larger than 24? What do these numbers refer to - values or indices? Extract the values by subsetting with thewhich()function and store them in a new variable .
x1<-X[,1]
x1[3]<-10
which(x1>24)## [1] 2 4 5a<-x1[which(x1>24)]
a## [1] 30 150 1500- Take the vector and prefix one element to it, the character “a”. Look at the vector. What changed? Replace the fourth value in with the character “b”. Set up a matrix with the first column being and the second column being . Explain why this works and why you get a message. What happened to
Ymat[,2]? Hint: Look at the last row. Remove the second element of and store that asz1and set upYmat1as you didYmat(i.e., combinez1andkto columns 1 and 2 ofYmat1). How didYmat1change as compared toYmat? Now set up a list with the first column being and the second column being . Explain why this works differently than forYmat. Now set up a data frameYdfwith columnszandk. Why does this not work? Now set upYdfwith columnsz1,k. How isYdfdifferent formYmat
z<-c(z,"a") #vector coerced to character
z ## [1] "15" "30" "45" "150" "1500" "a"z[4]<-"b"
Ymat<-cbind(z,k) #z has 6 elements, k has 5 ## Warning in cbind(z, k): number of rows of result is not a multiple of
## vector length (arg 2)Ymat #k gets recycled (recycling rule) so Ymat[6,2]=k[1] ## z k
## [1,] "15" "0"
## [2,] "30" "0.5"
## [3,] "45" "1.5"
## [4,] "b" "7.5"
## [5,] "1500" "100"
## [6,] "a" "0"z1<-z[-2]
Ymat1<-cbind(z1,k) #now z has 5 elements, k has 5
Ymat1 ## z1 k
## [1,] "15" "0"
## [2,] "45" "0.5"
## [3,] "b" "1.5"
## [4,] "1500" "7.5"
## [5,] "a" "100"Yl<-list(z,k) # is a list, elements can have different length Ydf<-data.frame(z,k) #z has 6 elements, k has 5; leads to error in data frame, no recycling Ydf<-data.frame(z1,k)
Ymat ## z k
## [1,] "15" "0"
## [2,] "30" "0.5"
## [3,] "45" "1.5"
## [4,] "b" "7.5"
## [5,] "1500" "100"
## [6,] "a" "0"class(Ymat[,1]) #Ymat[,1] is character## [1] "character"class(Ymat[,2]) #Ymat[,2] is also character## [1] "character"Ydf ## z1 k
## 1 15 0.0
## 2 45 0.5
## 3 b 1.5
## 4 1500 7.5
## 5 a 100.0class(Ydf[,1]) #Ydf[,1] is factor (data.frame automatically converts characters to factors ) ## [1] "factor"class(Ydf[,2]) #Ydf[,2] is numeric like k## [1] "numeric"- Use
dim()(or a similar function) to find out the number of columns and the number of rows in . Extract from the values in the first column, second row and fourth row, second column. Now extract the submatrix from the second row, first column to the next to last row, second column. Do this also for .
dim(Ymat)[2] #columns## [1] 2dim(Ydf)[1] #rows## [1] 5Ymat[c(2,4),c(1,2)]## z k
## [1,] "30" "0.5"
## [2,] "b" "7.5"Ymat[2:(nrow(Ymat)-1),c(1,2)]## z k
## [1,] "30" "0.5"
## [2,] "45" "1.5"
## [3,] "b" "7.5"
## [4,] "1500" "100"Ydf[c(2,4),c(1,2)]## z1 k
## 2 45 0.5
## 4 1500 7.5Ydf[2:(nrow(Ymat)-1),c(1,2)]## z1 k
## 2 45 0.5
## 3 b 1.5
## 4 1500 7.5
## 5 a 100.0- Download the course data set . Set the working directory to the directory where you saved the data. Look at the
bspdat.csvin an editor. What is the structure of the data (look particularly at the separation and decimal characters)? Read the dataset into R using theread.csv()orread.table()functions and save it as an object called . Investigate the structure of the object with and .
setwd("pathTo/bspdat.csv")bspdat<-read.table("bspdat.csv",header=TRUE,sep=";",dec=",")
head(bspdat)## age size weight female
## 1 29 173.8 73 0
## 2 21 179.7 69 0
## 3 20 162.5 60 1
## 4 29 174.6 69 1
## 5 25 163.3 55 1
## 6 30 181.4 72 0str(bspdat)## 'data.frame': 100 obs. of 4 variables:
## $ age : int 29 21 20 29 25 30 27 29 20 25 ...
## $ size : num 174 180 162 175 163 ...
## $ weight: int 73 69 60 69 55 72 67 73 69 59 ...
## $ female: int 0 0 1 1 1 0 1 0 1 0 ...- The data frame has a variable with values 1 for females and 0 for males. Save the data frame as
bspdat.rdawithsave(). Add a new variable to the data frame which should be called . It should be a factor with levels “male” for 0 and “female” for 1. Loadbspdat.rdaagain withload(). Does the object still contain the factor ?
save(bspdat,file="bspdat.rda")
gender<-factor(bspdat$female,labels=c("male","female"))
bspdat$gender<-gender
load(file="bspdat.rda")
bspdat$gender## NULL- There is a data file available in the
Exercise_01.Rdatafile. The object nameddatex1represents an unscored multiple choice test. Inspect the file withstr(),head()andsummary(). Do you find missing values? If so, replace them with 0. Is there something odd with the column names? Name the last column “gender”.
load('Exercise_01.Rdata')
head(datex1)## Item_1 Item_2 Item_3 Item_4 Item_5 Item_6 Item_7 Item_8 Item_9
## [1,] 4 3 1 3 3 2 5 3 2
## [2,] 0 3 0 3 0 0 0 0 4
## [3,] 0 0 2 0 0 2 2 0 2
## [4,] 4 3 4 3 3 4 5 5 2
## [5,] 0 3 0 0 0 2 3 2 2
## [6,] 3 0 2 0 0 5 0 4 3
## Item_10 Item_11 Item_12 Item_13 Item_14 Item_15 Item_16 Item_17
## [1,] 3 2 3 2 0 3 0 0
## [2,] 4 0 1 4 0 0 4 1
## [3,] 0 0 4 0 0 4 2 0
## [4,] 1 2 0 3 3 4 4 3
## [5,] 2 0 0 0 1 0 0 2
## [6,] 0 0 0 0 0 0 0 2
## Item_18 Item_19 Item_20 Item_21 Item_22 Item_23 Item_24 Item_25
## [1,] 3 4 2 0 1 1 3 0
## [2,] 0 0 0 2 0 2 3 4
## [3,] 0 0 0 1 1 0 0 0
## [4,] 1 4 2 4 1 4 3 4
## [5,] 0 2 4 3 0 0 1 0
## [6,] 0 0 4 3 0 3 2 2
## Item_26 Item_27 Item_28 Item_29 Item_30 Item_31 Item_32 Item_33
## [1,] 1 4 3 3 1 2 4 4
## [2,] 3 0 2 3 1 4 3 0
## [3,] 0 0 0 0 0 0 2 0
## [4,] 2 3 3 2 2 1 3 1
## [5,] 0 3 0 4 0 0 2 4
## [6,] 3 1 0 0 0 0 0 0
## Item_34 Item_35 Item_36 Item_37 Item_38 Item_39 Item_40 Item_41
## [1,] 4 2 0 4 1 3 4 2
## [2,] 0 0 0 4 4 4 2 0
## [3,] 0 0 0 0 0 0 0 0
## [4,] 1 2 3 4 0 1 4 5
## [5,] 0 0 0 0 0 4 4 0
## [6,] 0 0 5 1 0 0 3 0
## Item_42 Item_43 Item_44 Item_45 Item_46 Item_47 Item_48 Item_49
## [1,] 3 3 2 2 4 5 2 0
## [2,] 1 0 3 0 3 0 2 4
## [3,] 0 0 0 2 1 4 0 0
## [4,] 2 3 2 5 4 2 0 1
## [5,] 1 0 0 0 1 2 0 0
## [6,] 3 0 0 0 0 3 4 0
## Item_50
## [1,] 0 0
## [2,] 0 0
## [3,] 0 0
## [4,] 4 1
## [5,] 0 0
## [6,] 0 0str(datex1)## num [1:2500, 1:51] 4 0 0 4 0 3 4 4 1 2 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr [1:51] "Item_1" "Item_2" "Item_3" "Item_4" ...summary(datex1)## Item_1 Item_2 Item_3 Item_4
## Min. :0.000 Min. :0.000 Min. :0.0000 Min. :0.00
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.00
## Median :1.000 Median :3.000 Median :0.0000 Median :3.00
## Mean :1.576 Mean :1.681 Mean :0.9152 Mean :1.58
## 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:2.0000 3rd Qu.:3.00
## Max. :4.000 Max. :5.000 Max. :4.0000 Max. :5.00
## NA's :1
## Item_5 Item_6 Item_7 Item_8
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :0.000 Median :2.000 Median :0.000 Median :3.000
## Mean :1.547 Mean :1.822 Mean :1.533 Mean :2.365
## 3rd Qu.:3.000 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## NA's :1
## Item_9 Item_10 Item_11 Item_12
## Min. :0.000 Min. :0.00 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.00 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :0.00 Median :0.000 Median :1.000
## Mean :1.274 Mean :1.29 Mean :1.606 Mean :1.253
## 3rd Qu.:2.000 3rd Qu.:3.00 3rd Qu.:3.000 3rd Qu.:2.000
## Max. :4.000 Max. :4.00 Max. :5.000 Max. :4.000
## NA's :1 NA's :1
## Item_13 Item_14 Item_15 Item_16
## Min. :0.000 Min. :0.0000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :0.0000 Median :0.000 Median :2.000
## Mean :1.327 Mean :0.9856 Mean :1.542 Mean :1.873
## 3rd Qu.:3.000 3rd Qu.:2.0000 3rd Qu.:3.000 3rd Qu.:3.000
## Max. :4.000 Max. :4.0000 Max. :5.000 Max. :5.000
## NA's :2
## Item_17 Item_18 Item_19 Item_20
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :0.000 Median :1.000 Median :0.000
## Mean :1.188 Mean :1.118 Mean :1.621 Mean :1.033
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:2.000
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
## NA's :1
## Item_21 Item_22 Item_23 Item_24
## Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.000
## Median :0.0000 Median :1.0000 Median :1.000 Median :1.000
## Mean :0.8604 Mean :0.5752 Mean :1.363 Mean :1.636
## 3rd Qu.:2.0000 3rd Qu.:1.0000 3rd Qu.:3.000 3rd Qu.:3.000
## Max. :4.0000 Max. :5.0000 Max. :4.000 Max. :4.000
## NA's :2
## Item_25 Item_26 Item_27 Item_28
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :0.000 Median :1.000 Median :1.000
## Mean :1.288 Mean :1.114 Mean :1.502 Mean :1.282
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:3.000
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
##
## Item_29 Item_30 Item_31 Item_32
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :1.000 Median :1.000 Median :0.000
## Mean :1.378 Mean :1.226 Mean :1.259 Mean :1.172
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:3.000
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
##
## Item_33 Item_34 Item_35 Item_36
## Min. :0.000 Min. :0.0000 Min. :0.0000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000
## Median :0.000 Median :0.0000 Median :0.0000 Median :2.000
## Mean :1.135 Mean :0.9664 Mean :0.9804 Mean :1.918
## 3rd Qu.:2.000 3rd Qu.:2.0000 3rd Qu.:2.0000 3rd Qu.:4.000
## Max. :4.000 Max. :4.0000 Max. :4.0000 Max. :5.000
##
## Item_37 Item_38 Item_39 Item_40
## Min. :0.000 Min. :0.0000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :0.0000 Median :1.000 Median :2.000
## Mean :1.402 Mean :0.7655 Mean :1.493 Mean :1.821
## 3rd Qu.:3.000 3rd Qu.:1.0000 3rd Qu.:3.000 3rd Qu.:4.000
## Max. :4.000 Max. :4.0000 Max. :4.000 Max. :5.000
## NA's :1
## Item_41 Item_42 Item_43 Item_44
## Min. :0.00 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.00 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :0.00 Median :1.000 Median :1.000 Median :0.000
## Mean :1.13 Mean :1.247 Mean :1.481 Mean :1.209
## 3rd Qu.:3.00 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:2.000
## Max. :5.00 Max. :4.000 Max. :4.000 Max. :4.000
## NA's :1
## Item_45 Item_46 Item_47 Item_48
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :2.000 Median :1.000 Median :2.000 Median :1.000
## Mean :2.177 Mean :1.564 Mean :1.726 Mean :1.472
## 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000
## Max. :5.000 Max. :4.000 Max. :5.000 Max. :4.000
## NA's :1
## Item_49 Item_50 V51
## Min. :0.000 Min. :0.0000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.000
## Median :1.000 Median :0.0000 Median :1.000
## Mean :1.394 Mean :0.9548 Mean :0.526
## 3rd Qu.:3.000 3rd Qu.:2.0000 3rd Qu.:1.000
## Max. :4.000 Max. :4.0000 Max. :1.000
## NA's :1#Missings in Col 3,6,11,12,16,20,23,38,41,46,50
datex1[which(is.na(datex1),arr.ind = TRUE)]<-0
#or with a loop
#for(i in 1:dim(datex1)[2])
#{
# datex1[which(is.na(datex1[,i])),i]<-0
#}
colnames(datex1)[51]<-"gender"
summary(datex1)## Item_1 Item_2 Item_3 Item_4
## Min. :0.000 Min. :0.000 Min. :0.0000 Min. :0.00
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.00
## Median :1.000 Median :3.000 Median :0.0000 Median :3.00
## Mean :1.576 Mean :1.681 Mean :0.9148 Mean :1.58
## 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:2.0000 3rd Qu.:3.00
## Max. :4.000 Max. :5.000 Max. :4.0000 Max. :5.00
## Item_5 Item_6 Item_7 Item_8
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :0.000 Median :2.000 Median :0.000 Median :3.000
## Mean :1.547 Mean :1.822 Mean :1.533 Mean :2.365
## 3rd Qu.:3.000 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## Item_9 Item_10 Item_11 Item_12
## Min. :0.000 Min. :0.00 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.00 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :0.00 Median :0.000 Median :1.000
## Mean :1.274 Mean :1.29 Mean :1.605 Mean :1.252
## 3rd Qu.:2.000 3rd Qu.:3.00 3rd Qu.:3.000 3rd Qu.:2.000
## Max. :4.000 Max. :4.00 Max. :5.000 Max. :4.000
## Item_13 Item_14 Item_15 Item_16
## Min. :0.000 Min. :0.0000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :0.0000 Median :0.000 Median :2.000
## Mean :1.327 Mean :0.9856 Mean :1.542 Mean :1.871
## 3rd Qu.:3.000 3rd Qu.:2.0000 3rd Qu.:3.000 3rd Qu.:3.000
## Max. :4.000 Max. :4.0000 Max. :5.000 Max. :5.000
## Item_17 Item_18 Item_19 Item_20
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :0.000 Median :1.000 Median :0.000
## Mean :1.188 Mean :1.118 Mean :1.621 Mean :1.033
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:2.000
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
## Item_21 Item_22 Item_23 Item_24
## Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.000
## Median :0.0000 Median :1.0000 Median :1.000 Median :1.000
## Mean :0.8604 Mean :0.5752 Mean :1.362 Mean :1.636
## 3rd Qu.:2.0000 3rd Qu.:1.0000 3rd Qu.:3.000 3rd Qu.:3.000
## Max. :4.0000 Max. :5.0000 Max. :4.000 Max. :4.000
## Item_25 Item_26 Item_27 Item_28
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :0.000 Median :1.000 Median :1.000
## Mean :1.288 Mean :1.114 Mean :1.502 Mean :1.282
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:3.000
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
## Item_29 Item_30 Item_31 Item_32
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :1.000 Median :1.000 Median :0.000
## Mean :1.378 Mean :1.226 Mean :1.259 Mean :1.172
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:3.000
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
## Item_33 Item_34 Item_35 Item_36
## Min. :0.000 Min. :0.0000 Min. :0.0000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000
## Median :0.000 Median :0.0000 Median :0.0000 Median :2.000
## Mean :1.135 Mean :0.9664 Mean :0.9804 Mean :1.918
## 3rd Qu.:2.000 3rd Qu.:2.0000 3rd Qu.:2.0000 3rd Qu.:4.000
## Max. :4.000 Max. :4.0000 Max. :4.0000 Max. :5.000
## Item_37 Item_38 Item_39 Item_40
## Min. :0.000 Min. :0.0000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :0.0000 Median :1.000 Median :2.000
## Mean :1.402 Mean :0.7652 Mean :1.493 Mean :1.821
## 3rd Qu.:3.000 3rd Qu.:1.0000 3rd Qu.:3.000 3rd Qu.:4.000
## Max. :4.000 Max. :4.0000 Max. :4.000 Max. :5.000
## Item_41 Item_42 Item_43 Item_44
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :0.000 Median :1.000 Median :1.000 Median :0.000
## Mean :1.129 Mean :1.247 Mean :1.481 Mean :1.209
## 3rd Qu.:3.000 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:2.000
## Max. :5.000 Max. :4.000 Max. :4.000 Max. :4.000
## Item_45 Item_46 Item_47 Item_48
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :2.000 Median :1.000 Median :2.000 Median :1.000
## Mean :2.177 Mean :1.563 Mean :1.726 Mean :1.472
## 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000
## Max. :5.000 Max. :4.000 Max. :5.000 Max. :4.000
## Item_49 Item_50 gender
## Min. :0.000 Min. :0.0000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.000
## Median :1.000 Median :0.0000 Median :1.000
## Mean :1.394 Mean :0.9544 Mean :0.526
## 3rd Qu.:3.000 3rd Qu.:2.0000 3rd Qu.:1.000
## Max. :4.000 Max. :4.0000 Max. :1.000
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