Descriptive Statistics Guide: Central Tendency and Dispersion Metrics
Analyze numerical data sets with instantaneous statistical accuracy. Master arithmetic mean, median, mode, sample variance, and standard deviation for academic research, business financial audits, and laboratory experiments.
1. Measures of Central Tendency
Arithmetic Mean (Average)
The sum of all values divided by total count (x̄ = Σx / N). Highly sensitive to extreme outliers.
Median (Middle Value)
The middle value splitting ordered data into equal 50% halves. Highly resilient against skewed distributions like real estate prices and salary distributions.
Mode (Peak Frequency)
The most frequently repeated number in the series. Sets can be unimodal, bimodal, or multimodal.
2. Measures of Dispersion & Spread
Variance (s²)
The average of squared deviations from the mean. Expresses total data dispersion in squared units.
Standard Deviation (s)
The square root of variance. Expressed in the exact physical units of your raw measurements, modeling Gaussian bell curves (normal distribution).
Mathematical Reference Table
| Statistical Metric | Mathematical Formula | Practical Purpose |
|---|---|---|
| Data Range | Maximum Value - Minimum Value | Total spread between the lowest and highest values. |
| Sample Std Dev (s) | √[ Σ(x - x̄)² / (n - 1) ] | Applies Bessel's correction factor for unbiased sample estimation. |
Frequently Asked Questions
- How do I paste columns from Excel or Google Sheets?
- Simply copy a column of numerical cells and paste directly. The parser automatically cleans tab and newline delimiters to compute stats instantly.
- Why is standard deviation vital in quality control?
- A small standard deviation proves consistent manufacturing tolerances, whereas a large standard deviation alerts engineers to unstable process drift.