Descriptive Statistics in R

Descriptive statistics are essential tools for summarizing and understanding data in R. They provide insights into the central tendency, dispersion, and shape of your dataset.

Measures of Central Tendency

R offers several functions to calculate measures of central tendency:

Mean

The mean is the average of all values in a dataset. Calculate it using the mean() function:

data <- c(1, 2, 3, 4, 5)
mean_value <- mean(data)
print(mean_value)  # Output: 3

Median

The median is the middle value when the data is ordered. Use the median() function:

median_value <- median(data)
print(median_value)  # Output: 3

Mode

R doesn't have a built-in mode function, but you can create one:

get_mode <- function(x) {
  unique_x <- unique(x)
  unique_x[which.max(tabulate(match(x, unique_x)))]
}

mode_value <- get_mode(c(1, 2, 2, 3, 4, 4, 4, 5))
print(mode_value)  # Output: 4

Measures of Dispersion

These statistics describe the spread of your data:

Range

Calculate the range using range() or manually:

data_range <- max(data) - min(data)
print(data_range)  # Output: 4

Variance

Variance measures the average squared deviation from the mean. Use var():

variance <- var(data)
print(variance)  # Output: 2.5

Standard Deviation

The standard deviation is the square root of the variance. Calculate it with sd():

std_dev <- sd(data)
print(std_dev)  # Output: 1.581139

Measures of Shape

These statistics describe the distribution of your data:

Skewness

Skewness measures the asymmetry of the distribution. Use the moments package:

library(moments)
skewness_value <- skewness(data)
print(skewness_value)  # Output: 0

Kurtosis

Kurtosis measures the tailedness of the distribution:

kurtosis_value <- kurtosis(data)
print(kurtosis_value)  # Output: 1.7

Summary Statistics

R provides a convenient summary() function to get an overview of your data:

summary_stats <- summary(data)
print(summary_stats)

Visualizing Descriptive Statistics

Visualizations can help understand your data better. Use the ggplot2 package for creating informative plots:

library(ggplot2)

ggplot(data.frame(x = data), aes(x = x)) +
  geom_histogram(binwidth = 1, fill = "skyblue", color = "black") +
  geom_vline(aes(xintercept = mean(x)), color = "red", linetype = "dashed", size = 1) +
  labs(title = "Histogram with Mean", x = "Value", y = "Frequency")

Best Practices

• Always check for missing values before calculating statistics.
• Consider using robust statistics (e.g., median instead of mean) for skewed data.
• Visualize your data to get a better understanding of its distribution.
• Use the dplyr package for efficient data manipulation before analysis.

Mastering descriptive statistics in R is crucial for exploratory data analysis and lays the foundation for more advanced statistical techniques like hypothesis testing and regression analysis.