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

Source: Dev.to

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.

Objectives

• Summarize the data numerically
• Identify central tendency
• Measure variability (dispersion)
• Understand relative position of values
• Detect outliers
• Assess distribution shape
• Check data quality

Techniques Used in Uni‑variate Non‑Graphical EDA

Measures of Central Tendency

Describe the typical or centre value.

• Mean

  [ \bar{x}= \frac{\sum x}{n} ]

  Most common average; highly affected by outliers.

• Median – middle value of ordered data; resistant to extreme values.

• Mode – most frequent value; useful for discrete or categorical data.

Measures of Dispersion

Describe how spread out the data is.

• Range

  [ \text{Range}= \text{Max} - \text{Min} ]

• Variance

  [ \sigma^{2}= \frac{\sum (x-\bar{x})^{2}}{n} ]

• Standard Deviation

  [ \sigma = \sqrt{\sigma^{2}} ]

  Most widely used spread measure.

• Inter‑quartile Range (IQR)

  [ \text{IQR}= Q_{3} - Q_{1} ]

  Spread of the middle 50 %; less affected by outliers.

Measures of Position

Describe relative standing of values.

• Percentiles (e.g., P10, P50, P90)
• Quartiles (Q1, Q2, Q3)
• Deciles (D1 to D9)

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

Measures of Distribution Shape

• Skewness

  • Positive skew → right tail longer
  • Negative skew → left tail longer
  • Zero skew → symmetrical distribution

• Kurtosis – measures peakedness or tail thickness

  • Leptokurtic → sharp peak
  • Mesokurtic → normal (Gaussian)
  • Platykurtic → flat

More on distribution shape

Outlier Detection (Non‑Graphical)

IQR Method

[ \text{Lower limit}= Q_{1} - 1.5 \times \text{IQR} ]

[ \text{Upper limit}= Q_{3} + 1.5 \times \text{IQR} ]

Values outside these limits are considered outliers.

Z‑Score Method

[ z = \frac{x - \mu}{\sigma} ]

[ |z| > 3 ;; \rightarrow ;; \text{Potential outlier} ]

Data Quality Checks

Uni‑variate Non‑Graphical EDA helps detect:

• Missing values
• Invalid values (e.g., negative age)
• Extreme or impossible values
• Data entry errors

Advantages

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

Limitations

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

Example

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

• Mean = 20
• Median = 18
• Range = 30
• IQR = moderate (Q1 = 12, Q3 = 25 → IQR = 13)
• Skewness = positive (long right tail)
• Outlier = 40 (outside the IQR upper limit)

Conclusion

Uni‑variate Non‑Graphical Exploratory Data Analysis is a numerical approach to understand a single variable by analyzing its centre, spread, position, shape, and quality—without using graphs. It serves as a foundational step before more advanced statistical analysis.