Descriptive Statistics

Descriptive statistics summarize and organize the features of a dataset, providing simple summaries about the sample and the measures.

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1. Types of Descriptive Statistics

a. Measures of Central Tendency

• Mean: Average of all values

• Median: Middle value when data is ordered

• Mode: Most frequently occurring value

b. Measures of Dispersion

• Range: Difference between maximum and minimum values

• Variance: Average of squared deviations from the mean

• Standard Deviation (SD): Square root of variance

• Interquartile Range (IQR): Range between the 25th and 75th percentiles

c. Shape of the Distribution

• Skewness: Measure of asymmetry

• Kurtosis: Measure of peakedness

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2. Frequency Distribution

• Organizes data into classes or intervals

• Commonly visualized with histograms, bar charts, or frequency tables

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3. Visualizing Descriptive Statistics

• Histogram: Displays distribution of continuous variables

• Boxplot: Shows median, quartiles, and outliers

• Bar Chart: Visualizes categorical variable counts

# Example boxplot in R
boxplot(data$height)

# Histogram
hist(data$weight)

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4. Summary Statistics in R

# Basic summary
summary(data)

# Specific statistics
mean(data$score)
sd(data$score)
quantile(data$score, probs = c(0.25, 0.75))

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5. Summary

Descriptive statistics provide foundational insights into the data before applying more complex analyses. They are essential for understanding data distribution, detecting outliers, and informing appropriate statistical methods.