Descriptive Statistics and Probability Distributions

Before modeling anything, you need to summarize and understand your data. This lesson covers descriptive statistics and R's built-in support for probability distributions.

1. Measures of Central Tendency

x <- c(23, 45, 12, 67, 34, 89, 21, 45, 45)

mean(x)     # average
median(x)   # middle value
table(x)    # frequency table (mode is the most frequent value)

2. Measures of Spread

sd(x)          # standard deviation
var(x)         # variance
range(x)       # min and max
IQR(x)         # interquartile range
quantile(x)    # 0%, 25%, 50%, 75%, 100%

3. summary() — The Fast One-Liner

summary(x)
#    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
#   12.00   21.00   34.00   42.33   45.00   89.00

summary(df)   # works column-by-column on an entire data frame

4. Probability Distributions in R

R has four core functions for every distribution, following a consistent naming convention:

5. Working with the Normal Distribution

set.seed(42)                        # reproducibility
samples <- rnorm(1000, mean = 50, sd = 10)

hist(samples, breaks = 30, col = "skyblue",
     main = "Simulated Normal Distribution")

# Probability that a value is less than 60
pnorm(60, mean = 50, sd = 10)   # ~0.841

# 95th percentile value
qnorm(0.95, mean = 50, sd = 10)  # ~66.4

6. Other Common Distributions

# Probability of exactly 3 successes in 10 trials, p = 0.5
dbinom(3, size = 10, prob = 0.5)

# Simulate 5 coin-flip experiments
rbinom(5, size = 10, prob = 0.5)

7. Correlation Between Variables

cor(df$age, df$salary)                     # Pearson correlation coefficient
cor(df[, c("age", "salary", "experience")]) # correlation matrix

8. Production-Ready Checklist

• ✅ Master mean, median, sd, and quantile — the core summary statistics.
• ✅ Use summary() as your first exploratory step — on any new dataset.
• ✅ Know the d/p/q/r pattern — for working with any probability distribution.
• ✅ Always set.seed() — before random sampling, for reproducibility.