DESCRIPTIVE STATISTICS
Oumo David
2025-02-16
This is a tutorial on Descriptive statistics. Descriptive statistics summarize and organize characteristics of a dataset, providing insights into its distribution, central tendency, and variability. R offers various built-in functions and packages to perform descriptive statistics efficiently. In this tutorial, we will explore different methods to compute descriptive statistics in R.
1. Getting Started with R
Before we begin, ensure that R is installed on your system. You can also use RStudio for an enhanced coding experience.
To start, load the required packages: If not installed, install the following packages
install.packages(“dplyr”)
install.packages(“psych”)
Load the necessary packages
library(dplyr)## Warning: package 'dplyr' was built under R version 4.4.2##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(psych)## Warning: package 'psych' was built under R version 4.4.22. Creating a Sample Dataset
You can create a sample dataset using R’s built-in data.frame() function: Create a sample dataset View the dataset
data <- data.frame(
ID = 1:10,
Age = c(25, 30, 35, 40, 29, 33, 31, 27, 26, 32),
Salary = c(40000, 50000, 60000, 70000, 45000, 55000, 52000, 47000, 43000, 51000)
)
print(data)## ID Age Salary
## 1 1 25 40000
## 2 2 30 50000
## 3 3 35 60000
## 4 4 40 70000
## 5 5 29 45000
## 6 6 33 55000
## 7 7 31 52000
## 8 8 27 47000
## 9 9 26 43000
## 10 10 32 510003. Measures of Central Tendency
Central tendency describes the center point of a dataset. Common measures include:
Mean (Average)
mean_age <- mean(data$Age)
mean_salary <- mean(data$Salary)Median (Middle Value)
median_age <- median(data$Age)
median_salary <- median(data$Salary)Mode (Most Frequent Value)
mode_function <- function(x) {
uniq_x <- unique(x)
uniq_x[which.max(tabulate(match(x, uniq_x)))]
}
mode_age <- mode_function(data$Age)Display results
Mean age, Median age, Mode_age
Mean salary, Median salary
mean_age; median_age; mode_age## [1] 30.8## [1] 30.5## [1] 25mean_salary; median_salary## [1] 51300## [1] 505004. Measures of Dispersion
Dispersion indicates how data values spread around the central value.
Standard Deviation
sd_age <- sd(data$Age)
sd_salary <- sd(data$Salary)Variance
var_age <- var(data$Age)
var_salary <- var(data$Salary)Range
range_age <- range(data$Age)
range_salary <- range(data$Salary)Interquartile Range (IQR)
iqr_age <- IQR(data$Age)
iqr_salary <- IQR(data$Salary)Display results
sd_age, var_age, range_age, iqr_age
sd_salary, var_salary, range_salary, iqr_salary
sd_age; var_age; range_age; iqr_age## [1] 4.516636## [1] 20.4## [1] 25 40## [1] 5.25sd_salary; var_salary; range_salary; iqr_salary## [1] 8794.569## [1] 77344444## [1] 40000 70000## [1] 87505. Summary Statistics Using Built-in Functions
R provides built-in functions for quick summaries: Summary function
summary(data)## ID Age Salary
## Min. : 1.00 Min. :25.00 Min. :40000
## 1st Qu.: 3.25 1st Qu.:27.50 1st Qu.:45500
## Median : 5.50 Median :30.50 Median :50500
## Mean : 5.50 Mean :30.80 Mean :51300
## 3rd Qu.: 7.75 3rd Qu.:32.75 3rd Qu.:54250
## Max. :10.00 Max. :40.00 Max. :700006. Using psych Package for Enhanced Descriptive Statistics
The describe() function from the psych package provides detailed statistics:
describe(data)## vars n mean sd median trimmed mad min max range skew
## ID 1 10 5.5 3.03 5.5 5.50 3.71 1 10 9 0.00
## Age 2 10 30.8 4.52 30.5 30.38 4.45 25 40 15 0.54
## Salary 3 10 51300.0 8794.57 50500.0 50375.00 7413.00 40000 70000 30000 0.72
## kurtosis se
## ID -1.56 0.96
## Age -0.75 1.43
## Salary -0.47 2781.097. Visualizing Data
Visualizations help understand data distribution.
Histogram
hist(data$Age, main="Age Distribution", xlab="Age", col="blue", breaks=5)
Boxplot
boxplot(data$Salary, main="Salary Distribution", ylab="Salary", col="red")
Descriptive statistics provide essential insights into datasets before conducting further analysis. R offers various functions and packages to compute these statistics efficiently. By understanding central tendency, dispersion, and visualization techniques, you can effectively summarize and interpret data.
8.Descriptive statistics on the mtcars dataset
Now, let us look at the mtcars dataset to explore the descriptive statistics
Load built-in dataset Assign it to a variable
data("mtcars")
df <- mtcars9. Overview of the Dataset
To understand the dataset structure.
View first few rows
head(df)## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1Check the structure
str(df)## 'data.frame': 32 obs. of 11 variables:
## $ mpg : num 21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
## $ cyl : num 6 6 4 6 8 6 8 4 4 6 ...
## $ disp: num 160 160 108 258 360 ...
## $ hp : num 110 110 93 110 175 105 245 62 95 123 ...
## $ drat: num 3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
## $ wt : num 2.62 2.88 2.32 3.21 3.44 ...
## $ qsec: num 16.5 17 18.6 19.4 17 ...
## $ vs : num 0 0 1 1 0 1 0 1 1 1 ...
## $ am : num 1 1 1 0 0 0 0 0 0 0 ...
## $ gear: num 4 4 4 3 3 3 3 4 4 4 ...
## $ carb: num 4 4 1 1 2 1 4 2 2 4 ...Summary statistics
summary(df)## mpg cyl disp hp
## Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0
## 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5
## Median :19.20 Median :6.000 Median :196.3 Median :123.0
## Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7
## 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0
## Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0
## drat wt qsec vs
## Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000
## 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000
## Median :3.695 Median :3.325 Median :17.71 Median :0.0000
## Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375
## 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000
## Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000
## am gear carb
## Min. :0.0000 Min. :3.000 Min. :1.000
## 1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000
## Median :0.0000 Median :4.000 Median :2.000
## Mean :0.4062 Mean :3.688 Mean :2.812
## 3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :1.0000 Max. :5.000 Max. :8.00010. Measures of Central Tendency
These include the mean, median, and mode.
Mean Mean of miles per gallon
mean(df$mpg) ## [1] 20.09062Median Median of miles per gallon
median(df$mpg) ## [1] 19.2Mode (Custom function, since R has no built-in mode function)
mode_func <- function(x) {
uniq_vals <- unique(x)
uniq_vals[which.max(tabulate(match(x, uniq_vals)))]
}
mode_func(df$mpg)## [1] 2111. Measures of Dispersion
These include the range, variance, standard deviation, and interquartile range (IQR).
Range
range(df$mpg)## [1] 10.4 33.9Variance
var(df$mpg)## [1] 36.3241Standard deviation
sd(df$mpg)## [1] 6.026948Interquartile Range (IQR)
IQR(df$mpg)## [1] 7.37512. Skewness and Kurtosis
Skewness measures symmetry, and kurtosis measures the “tailedness” of the distribution.
Load necessary library
library(moments)Skewness
skewness(df$mpg)## [1] 0.6404399Kurtosis
kurtosis(df$mpg)## [1] 2.79946713. Frequency Distribution (Categorical Data)
For categorical data, we use tables and proportions.
Convert a numerical variable into a categorical one
df$cyl_factor <- as.factor(df$cyl)Frequency table
table(df$cyl_factor)##
## 4 6 8
## 11 7 14Proportion table
prop.table(table(df$cyl_factor))##
## 4 6 8
## 0.34375 0.21875 0.4375014. Visualizing Data
Histograms
hist(df$mpg, main="Histogram of MPG", xlab="Miles per Gallon", col="blue")
Boxplot
boxplot(df$mpg, main="Boxplot of MPG", ylab="Miles per Gallon", col="red")
Bar Chart (for categorical data)
barplot(table(df$cyl_factor), main="Cylinder Count", col="green")
15. Summary Statistics for Multiple Columns
Summary statistics for all numerical variables
summary(df)## mpg cyl disp hp
## Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0
## 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5
## Median :19.20 Median :6.000 Median :196.3 Median :123.0
## Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7
## 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0
## Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0
## drat wt qsec vs
## Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000
## 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000
## Median :3.695 Median :3.325 Median :17.71 Median :0.0000
## Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375
## 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000
## Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000
## am gear carb cyl_factor
## Min. :0.0000 Min. :3.000 Min. :1.000 4:11
## 1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000 6: 7
## Median :0.0000 Median :4.000 Median :2.000 8:14
## Mean :0.4062 Mean :3.688 Mean :2.812
## 3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :1.0000 Max. :5.000 Max. :8.000Apply functions across multiple columns Mean for all numeric columns
sapply(df[, sapply(df, is.numeric)], mean)## mpg cyl disp hp drat wt qsec
## 20.090625 6.187500 230.721875 146.687500 3.596563 3.217250 17.848750
## vs am gear carb
## 0.437500 0.406250 3.687500 2.812500Conclusion
This tutorial introduced key descriptive statistics in R, including measures of central tendency, dispersion, skewness, and visualizations. These techniques help summarize and understand data effectively.