1.1.2 Univariate Analysis (Detailed Explanation)

Univariate Analysis is a type of exploratory data analysis where only one variable is examined at a time.
The goal is to understand the basic characteristics of that variable—its distribution, central value, spread, and overall behavior.

“Uni” means “one,” so univariate analysis answers questions about a single column in the dataset.

Why Do We Use Univariate Analysis?

Univariate analysis helps you understand:

• What values the variable takes

• How those values are distributed

• Whether the data is skewed or normal

• Whether there are outliers

• What the typical (central) value is

• How spread out the data is

It is the foundation of data understanding before moving to more advanced steps like bivariate or multivariate analysis.

Types of Variables in Univariate Analysis

Univariate analysis differs depending on the type of variable:

1. Numerical (Quantitative) Variables

These variables contain numbers.
Examples: marks, height, weight, salary, age.

Two types:

• Continuous data: decimals possible (e.g., height = 172.5 cm)

• Discrete data: whole numbers (e.g., number of students = 45)

2. Categorical (Qualitative) Variables

These variables contain text/labels instead of numbers.
Examples: gender, city, preferred product, blood group.

Two types:

• Nominal: no order (e.g., Red, Blue, Green)

• Ordinal: ordered categories (e.g., Grade A, B, C)

Univariate Analysis Techniques for Numerical Data

A. Measures of Central Tendency

These describe the “center” of the data.

1. Mean (Average)

Sum of values ÷ number of values
Example:
Ages = [10, 12, 14]
Mean = (10 + 12 + 14) / 3 = 12

2. Median (Middle Value)

Sorted dataset’s center value.
Example:
Data = [5, 7, 9]
Median = 7

3. Mode (Most Frequent Value)

Example:
Data = [2, 2, 3, 4]
Mode = 2

B. Measures of Dispersion (Spread of Data)

1. Range

Max – Min
Example: 90 – 20 = 70

2. Variance

Average squared difference from mean.

3. Standard Deviation

Square root of variance.
Higher SD = more spread out data.

C. Shape of the Distribution

Univariate analysis checks:

• Skewness (left/right skew)

• Kurtosis (peakedness/flatness)

• Normal distribution

Example:
Salary data is usually right-skewed because few people earn very high salaries.

D. Visual Tools for Numerical Univariate Analysis

1. Histogram

Shows how frequently values appear in different ranges.

2. Box Plot

Shows median, quartiles, and outliers.

3. Density Plot

Smooth version of a histogram.

Example:

Data: Marks = [40, 50, 60, 70, 100]

• Histogram shows distribution

• Box plot highlights 100 as an outlier

Univariate Analysis Techniques for Categorical Data

A. Frequency Distribution

Count how many times each category appears.

Example:
Fruits Bought:

• Apple: 30

• Banana: 20

• Mango: 10

B. Percentage Distribution

Percentage for each class.

Apple → 30 / (30+20+10) = 50%

C. Mode

Most frequent category.
Here: Apple

Visual Tools for Categorical Data

1. Bar Chart

Best for comparing category frequencies.

2. Pie Chart

Displays proportions.

3. Donut Chart

Alternative to a pie chart.

Real-life Example of Univariate Analysis

Dataset: Monthly Salaries (in ₹)

[20,000, 22,000, 25,000, 27,000, 40,000, 90,000]

Univariate Analysis Gives:

• Mean = 37,166

• Median = 26,000

• Mode = None

• Range = 90,000 – 20,000 = 70,000

• SD = Large (high variation)

• Outlier = 90,000

• Distribution = Right-skewed

This helps to understand that most salaries are between 20k–40k except one very high value.

Importance of Univariate Analysis

• Helps understand each variable individually

• Supports decision-making

• Helps in cleaning data (detect missing values/outliers)

• Essential for selecting modeling techniques

• Helps decide binning, transformation, or normalization