R Descriptive Statistics

Descriptive statistics summarize and describe the main features of a dataset using numbers. They answer basic questions about your data before any modeling: What is the typical value? How spread out are the values? What is the shape of the distribution? R calculates all standard descriptive statistics in one or two lines.

Measures of Central Tendency

scores <- c(55, 70, 72, 75, 78, 80, 82, 85, 88, 90, 92, 95, 45, 100, 68)

mean(scores)     # 78.33 — arithmetic average
median(scores)   # 80    — middle value when sorted

# Mode — most frequent value (no built-in function, write your own)
mode_val <- function(x) {
  tab <- table(x)
  as.numeric(names(tab)[tab == max(tab)])
}

Central Tendency Diagram:
  Sorted: 45 55 68 70 72 75 78 80 82 85 88 90 92 95 100
                              ↑
                           Median = 80

  Mean = (sum of all) / 15 = 78.33

  Median vs Mean:
    Symmetric data:  mean ≈ median
    Right-skewed:    mean > median  (e.g. incomes)
    Left-skewed:     mean < median

Measures of Spread

var(scores)    # 218.52 — variance (average squared deviation)
sd(scores)     # 14.78  — standard deviation (in original units)
range(scores)  # 45 100 — min and max
diff(range(scores))  # 55 — range width

IQR(scores)    # 20 — interquartile range (Q3 - Q1)
mad(scores)    # median absolute deviation

Quantiles and Percentiles

quantile(scores)           # 0%, 25%, 50%, 75%, 100%
quantile(scores, 0.25)     # Q1 = 70
quantile(scores, 0.75)     # Q3 = 90
quantile(scores, c(0.1, 0.9))   # 10th and 90th percentile

# Custom percentiles
quantile(scores, probs=seq(0, 1, 0.2))

Box-and-whisker representation of quantiles:
  Q0   Q1     Q2    Q3   Q4
  |────|───────|─────|────|
  45   70     80    90   100
       └──────────────┘
           IQR = 20

summary() — One-Call Overview

summary(scores)
#    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
#    45.0    70.0    80.0    78.3    90.0   100.0

Skewness and Kurtosis

library(e1071)

skewness(scores)   # < 0: left-skewed, > 0: right-skewed, ≈ 0: symmetric
kurtosis(scores)   # measures tail heaviness

Skewness guide:
  -0.5 to 0.5  → roughly symmetric
  0.5 to 1.0   → moderately right-skewed
  > 1.0        → highly right-skewed

Descriptive Stats for a Data Frame

students <- data.frame(
  age    = c(20,22,21,25,23,24,22,21,26,20),
  score  = c(78,85,72,90,68,88,75,80,92,65),
  salary = c(25000,35000,28000,45000,30000,40000,32000,38000,50000,27000)
)

summary(students)
#       age            score           salary
#  Min.   :20.0   Min.   :65.0   Min.   :25000
#  1st Qu.:21.0   1st Qu.:74.2   1st Qu.:28500
#  Median :22.0   Median :79.5   Median :33500
#  Mean   :22.4   Mean   :79.3   Mean   :35000
#  3rd Qu.:23.8   3rd Qu.:86.8   3rd Qu.:39500
#  Max.   :26.0   Max.   :92.0   Max.   :50000

# All stats at once per column
sapply(students, function(x) c(
  mean=mean(x), sd=round(sd(x),2),
  min=min(x), max=max(x), median=median(x)
))

Frequency Tables

grades <- c("A","B","A","C","B","A","D","B","A","C")

table(grades)
#grades
# A B C D
# 4 3 2 1

prop.table(table(grades))   # proportions
#grades
#    A    B    C    D
#  0.4  0.3  0.2  0.1

Correlation Overview

cor(students$age, students$score)     # single pair
cor(students)                          # full correlation matrix

Descriptive statistics are always the first step in any analysis. Before fitting a model or creating a visualization, run summary() on your data frame and check distributions, ranges, and missing value counts. These numbers tell you what you are working with and flag any issues before they cause problems downstream.