In R, the functions apply(), lapply(), sapply(), and tapply() are used to apply a function to elements of a vector, matrix, list or data frame.

apply(): This function applies a function to a matrix or an array. It returns a vector or an array with the results. As researched by **R Programming Assignment Help** team, The first argument to apply() is the matrix or array to which the function is to be applied. The second argument is the margin, either 1 or 2, that specifies whether the function should be applied to the rows or columns of the matrix.

Example:

Suppose you have a matrix mat with 3 rows and 4 columns, and you want to find the mean of each column. You can use the apply() function as follows:

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mat <- matrix(c(1:12), nrow = 3, ncol = 4)

apply(mat, 2, mean)

This will return a vector with the mean of each column of the matrix.

lapply(): This function applies a function to each element of a list and returns a list with the results. The first argument to lapply() is the list to which the function is to be applied. The second argument is the function to be applied.

Example:

Suppose you have a list lst with three vectors, and you want to find the length of each vector. You can use the lapply() function as follows:

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lst <- list(c(1, 2, 3), c(4, 5), c(6, 7, 8, 9))

lapply(lst, length)

This will return a list with the length of each vector in the list.

sapply(): This function is similar to lapply(), but it simplifies the result to a vector or matrix if possible. The first argument to sapply() is the list to which the function is to be applied. The second argument is the function to be applied.

Example:

Suppose you have a list lst with three vectors, and you want to find the length of each vector. You can use the sapply() function as follows:

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lst <- list(c(1, 2, 3), c(4, 5), c(6, 7, 8, 9))

sapply(lst, length)

This will return a vector with the length of each vector in the list.

tapply(): This function applies a function to subsets of a vector or a factor. The first argument to tapply() is the vector to which the function is to be applied. The second argument is the factor that defines the subsets. The third argument is the function to be applied.

Example:

Suppose you have a vector vec with the scores of 10 students on a test, and you want to find the mean score for each grade level. You can use the tapply() function as follows:

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vec <- c(70, 75, 80, 85, 90, 65, 70, 75, 80, 85)

grades <- factor(c(“A”, “B”, “B”, “B”, “A”, “C”, “C”, “B”, “C”, “A”))

tapply(vec, grades, mean)

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As considered by **Statistics Homework Help** team of experts, This will return a vector with the mean score for each grade level.