BCA PART B 3.R program to calculate coefficient of variance for discrete & continuous series

 Coefficient of Variation (CV) is defined as the ratio of the standard deviation (σ) to the mean (μ) and is usually expressed as a percentage:

$$CV = \left(\frac{\sigma}{\mu}\right) \times 100$$

Program :

# Function to calculate Coefficient of Variation for a Discrete Series

cv_discrete <- function(x) {

  mean_val <- mean(x)

  sd_val <- sd(x)

 

  cv <- (sd_val / mean_val) * 100

  return(cv)

}

# Function to calculate Coefficient of Variation for a Continuous Series

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

  # Calculate midpoints of the class intervals

  midpoints <- (lower_bound + upper_bound) / 2

 

  # Calculate the mean for the continuous series

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

 

  # Calculate variance

  variance <- sum(frequency * (midpoints - mean_val)^2) / sum(frequency)

 

  # Calculate standard deviation

  sd_val <- sqrt(variance)

 

  # Calculate Coefficient of Variation

  cv <- (sd_val / mean_val) * 100

  return(cv)

}

# Example Usage for Discrete Series:

discrete_data <- c(10, 20, 30, 40, 50)  # Example values for discrete series

cv_discrete(discrete_data)

# Example Usage for Continuous Series:

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

cv_continuous(lower_bound, upper_bound, frequency)

Output :

52.704627669473

49.4769730650902

Explanation:

• Discrete Series:
  • cv_discrete: This function takes a vector x of discrete values and computes the coefficient of variation using the mean and sd (standard deviation) functions in R.
• Continuous Series:
  • cv_continuous: This function takes three inputs:
    • lower_bound: A vector of the lower bounds of class intervals.
    • upper_bound: A vector of the upper bounds of class intervals.
    • frequency: A vector of frequencies for each class interval.
  • It calculates the midpoint of each class interval, then computes the mean and standard deviation of the data and finally calculates the coefficient of variation.