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I have a base that shows me the answers of the applicants to a course. The original base is 2k rows and 105 columns, of which 100 correspond to questions from 4 basic areas of mathematics, language, science, and social.

I have created the following short example so that you can see more or less how the table is

```
sector<-c("Privado" ,"Publico" ,"Publico" ,"Publico", "Publico",
"Publico" ,"Publico", "Publico", "Publico" ,"Publico", "Publico",
"Publico" ,"Publico", "Publico", "Publico" ,"Privado" ,"Publico" ,
"Publico" ,"Publico" ,"Publico")
aspirante<-c("337877" ,"339161", "388425" ,"371828" ,"288598" ,"396295" ,"400196",
"370915", "276891" ,"335406" ,"358013", "404406", "356633", "284792", "372549" ,
"271082", "396135" ,"398664" ,"406397", "354609")
claves<-c("10" ,"9" , "10", "4" , "4" , "3" , "3" , "4" , "9" ,"10", "3",
"3" , "3" , "4" , "4" , "4" , "4", "4" ,"9" , "3")
question1<-c(1, 0, 0, 0 ,0, 0, 0, 0, 0 ,0, 0, 0 ,0, 0, 0 ,0, 0, 0 ,1, 0)
question2<-c(0, 1, 1 ,0 ,0, 0 ,0 ,0 ,1, 0, 0,0,1 ,0 ,1, 1, 0 ,0, 0, 0)
question3<-c( 0 ,0, 1, 1, 1 ,1 ,0, 0, 0 ,0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0)
question4<-c(0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1)
question5<-c(1, 0, 1, 0 ,0, 1, 0, 1, 1, 0, 1, 1, 0 ,0 ,0, 0, 1, 0, 0, 0)
note<-c(4 ,2, 6, 4, 2, 6, 0 ,4, 4 ,0, 4 ,4 ,6, 2, 4 ,4, 4, 2, 4, 2)
example<-data.frame("candidate"=aspirante,"sector"=sector,"p1"=question1,
"p2"=question2,"p3"=question3,"p4"=question4,"p5"=question5,"note"=note)
```

I am asked to do a cluster analysis but I have no idea what to do, I had planned to divide the final notes into 4 categories:

failed: grades less than 3

considered: between 3 and 5

space availability: between 5 and 7

approved: from 7 to 10

but in the original base the sizes of each will vary and I cannot create a new base that divides the notes by group. Do you have any suggestions or an example where cluster analysis is applied to dichotomous data?

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