STATISTICS - Uni-variate Non-Graphical Exploratory Data Analysis (EDA)

Uni-variate Non-Graphical Exploratory Data Analysis (EDA)

Uni-variate Non-Graphical EDA is the numerical examination of a single variable without using charts or graphs. The goal is to understand the data’s central value, spread, position, shape, and quality using statistical measures.

1. Meaning

Uni-variate → Only one variable is analyzed

Non-Graphical → Uses numbers and statistics, not plots

Exploratory → No assumptions; aims to discover patterns, anomalies, and summaries

📌 Example variables: exam marks, age, income, daily sales, temperature.

1. Objectives

Summarize the data numerically

Identify central tendency

Measure variability (dispersion)

Understand relative position of values

Detect outliers

Assess distribution shape

Check data quality

1. Techniques Used in Uni-variate Non-Graphical EDA A. Measures of Central Tendency

Describe the typical or center value.

1. Mean 𝑥ˉ=∑𝑥𝑛xˉ=n∑x ​

Most common average

Highly affected by outliers

1. Median

Middle value of ordered data

Resistant to extreme values

1. Mode

Most frequent value

Useful for discrete or categorical data

B. Measures of Dispersion

Describe how spread out the data is.

1. Range Range = Max − Min Range=Max−Min

2. Variance
   𝜎2=∑(𝑥−𝑥ˉ)2𝑛σ2=n∑(x−xˉ)2
   ​

3. Standard Deviation
   𝜎=𝜎2σ=σ2
   ​

Most widely used spread measure

1. Inter-quartile Range (IQR)
   IQR=𝑄3−𝑄1

   ​
   Spread of middle 50%

Less affected by outliers

C. Measures of Position

Describe relative standing of values.

Percentiles (P10, P50, P90)

Quartiles (Q1, Q2, Q3)

Deciles (D1 to D9)

📌 Example: 75th percentile means 75% of data lies below it.

D. Measures of Distribution Shape :

1. Skewness

Positive skew → Right tail longer

Negative skew → Left tail longer

Zero skew → Symmetrical distribution

1. Kurtosis

Measures peakedness or tail thickness

Leptokurtic → Sharp peak

Mesokurtic → Normal

Platykurtic → Flat

1. Outlier Detection (Non-Graphical) IQR Method Lower limit =𝑄1−1.5(IQR) Lower limit=Q1−1.5(IQR) Upper limit=𝑄3+1.5(IQR)

Values outside → Outliers

Z-Score Method
𝑧=𝑥−𝜇/𝜎
​
|z| > 3 → Potential outlier

1. Data Quality Checks

Uni-variate Non-Graphical EDA helps detect:

Missing values

Invalid values (negative age)

Extreme or impossible values

Data entry errors

1. Advantages

✔ Simple and fast
✔ No visualization required
✔ Works well for summaries
✔ Ideal for exam and theory questions

1. Limitations

✖ No visual insight
✖ Cannot show trends
✖ Less intuitive for large datasets

1. Example

Data: 10, 12, 15, 18, 20, 25, 40

Mean = 20

Median = 18

Range = 30

IQR = Moderate

Skewness = Positive

Outlier = 40

1. Conclusion

Uni-variate Non-Graphical Exploratory Data Analysis is a numerical approach to understand a single variable by analyzing its center, spread, position, shape, and quality—without using graphs. It is a foundation step before advanced statistical analysis.

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