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Statistics Calculator — Descriptive Stats, Quartiles & IQR
Calculate comprehensive descriptive statistics for any dataset: mean, median, modes, quartiles (Q1, Q3), interquartile range (IQR), variance, standard deviation, and frequency distributions.
DMaintained by Data & Statistics Desk
Published
Paste data from Excel or text files. Decimals, positive, and negative numbers are accepted.
Descriptive Statistics Summary
Enter at least one number on the left to view comprehensive statistics.
DMaintained by Data & Statistics Desk
Published
Calculation Methodology & Formula
Calculates central tendency and dispersion metrics using linear interpolation percentiles and Bessel-corrected sample statistics.
\text{IQR} = Q_3 - Q_1 \quad \Big| \quad s = \sqrt{\frac{1}{N - 1} \sum_{i=1}^N (x_i - \bar{x})^2} \quad \Big| \quad \text{SE} = \frac{s}{\sqrt{N}}Worked Example: Research Survey Data Analysis
Calculate statistical dispersion and quartiles for test scores: 12, 15, 18, 22, 25, 28, 30, 32.
dataset:12, 15, 18, 22, 25, 28, 30, 32
Expected OutputMean: 22.75, Median: 23.5, Q1: 17.25, Q3: 28.5, IQR: 11.25, Std Dev: 7.15
Uses continuous linear interpolation (R-7) to determine exact quartiles and dispersion.
Technical Constraints & Limitations
- Harmonic and geometric means require all values to be strictly positive (> 0).
- Skewness and sample standard deviation require at least 3 distinct values for statistical significance.
Frequently Asked Questions
What is the Interquartile Range (IQR)?
The IQR is the distance between the 75th percentile (Q3) and the 25th percentile (Q1). It measures the spread of the middle 50% of your data and is resistant to extreme outliers.
How are percentiles calculated in this tool?
We use Method R-7 (standard in Excel PERCENTILE.INC and R), which uses linear interpolation between the data points closest to the rank index.
What is Skewness?
Skewness measures the asymmetry of your data distribution. A skewness of 0 indicates a symmetrical bell curve, positive values indicate a right-leaning tail, and negative values indicate a left-leaning tail.