BCA PART B 5.R program to calculate arithmetic mean for grouped and ungrouped data

1. Ungrouped Data (mean_ungrouped):

   • The mean_ungrouped function computes the mean of a vector of data using the mean() function, which calculates the sum of all values divided by the number of values.

2. Grouped Data (mean_grouped):

   • For grouped data, we first calculate the midpoints of each class interval using the formula: $$\text{midpoint} = \frac{\text{lower bound} + \text{upper bound}}{2}$$
   • Then, we compute the arithmetic mean using the frequency-weighted mean formula: $$\text{Mean} = \frac{\sum (\text{midpoint} \times \text{frequency})}{\sum \text{frequency}}$$

Program:

# Function to calculate arithmetic mean for ungrouped data

mean_ungrouped <- function(data) {

  mean_val <- mean(data)

  return(mean_val)

}

# Function to calculate arithmetic mean for grouped data

mean_grouped <- function(lower_bound, upper_bound, frequency) {

  # Calculate midpoints of the class intervals

  midpoints <- (lower_bound + upper_bound) / 2

 

  # Calculate the weighted mean for the grouped data

  mean_val <- sum(midpoints * frequency) / sum(frequency)

 

  return(mean_val)

}

# Example Usage for Ungrouped Data

ungrouped_data <- c(10, 20, 30, 40, 50)  # Example ungrouped data

cat("Arithmetic Mean for Ungrouped Data:\n")

print(mean_ungrouped(ungrouped_data))

# Example Usage for Grouped Data

lower_bound <- c(0, 10, 20, 30)  # Lower bounds of class intervals

upper_bound <- c(10, 20, 30, 40) # Upper bounds of class intervals

frequency <- c(5, 10, 8, 7)      # Frequency of each class interval

cat("\nArithmetic Mean for Grouped Data:\n")

print(mean_grouped(lower_bound, upper_bound, frequency))

Output:

Arithmetic Mean for Ungrouped Data:

[1] 30

Arithmetic Mean for Grouped Data:

[1] 20