Question

Write a function in R named counts.

This function should take as parameters a numeric vector x and also a number indicating a number of bins n. The function will consider the range [min(x),max(x)], and then consider a parti- tion of this interval into n non-overlapping equally sized half open intervals: I1 = [min(x),b1),I2 = [b1,b − 2),...,In = (bn−1,max(x)].

Note that since the intervals are equally sized, the value of bi is constrained. The function will then return a vector of length n such that the i-th element of this vector is the number of coordinates of x that lie in the interval Ii. Provide the code for this function: It should be of the following form:

counts = function(...) {

...

return(...)

}

Thank you for your help.

Answer 1

Here we have fixed a width of a class by dividing the range with the number of bins.

Then the bins are formed as given in the problem.

The R-code for this problem is,

counts <- function(x,n){
   width <- (max(x)-min(x))/n
   b <- array(dim=1)
   b[1] <- min(x)+width
   for(i in 2:(n-1)){
       b[i] <- b[i-1]+width
   }
   #lower class limit
   lcl <- c(min(x),b)
   #upper class limit     
   ucl <- c(b,max(x))
   frequency <- rep(0,n)
   for(i in 1:length(x)){
       if(x[i]==max(x))
           frequency[n] <- frequency[n] +1
       for(j in 1:n){
           if(lcl[j]<=x[i] && ucl[j]>x[i])
               frequency[j] <- frequency[j] + 1
       }
   }
   return(frequency)
}

The above program returns only the vector of frequency for a class. If we want to change it such that the lower and upper class limits, then we have to change the return part of the function to,

return(data.frame(lcl,ucl,frequency))

An example x and n, with the function is shown below,
counts(seq(1:11),4)