Descriptive Statistics Calculator
Enter a dataset to compute key descriptive statistics, quartiles, and measures of spread.
Mean
24.0000
Median
24.0000
Range
24.0000
Count: 9
Minimum: 12.0000
Maximum: 36.0000
Mode(s): No mode (all unique)
Dispersion
- Population variance: 60.0000
- Population std. dev.: 7.7460
- Sample variance: 67.5000
- Sample std. dev.: 8.2158
Quartiles
- Q1: 18.0000
- Median (Q2): 24.0000
- Q3: 30.0000
- Interquartile Range (IQR): 12.0000
How to Use This Calculator
- Input numeric observations separated by spaces or commas.
- Review location statistics (mean, median, mode) and dispersion measures.
- Use quartiles and IQR to understand distribution spread and identify outliers.
- Export results or use them to populate reports, dashboards, or further analyses.
Formula
Mean μ = Σxi / n
Variance σ² = Σ(xi − μ)² / n
Sample variance s² = Σ(xi − μ)² / (n − 1)
Median = middle value(s) when data sorted
Mode = value(s) with highest frequency
IQR = Q3 − Q1
These statistics describe central tendency, spread, and shape, providing a holistic view of your dataset.
Full Description
Descriptive statistics summarize datasets before modeling or inference. They reveal typical values, variation, and distribution shape, helping analysts detect anomalies or compare multiple datasets quickly.
Combining numerical summaries with plots (histograms, box plots) enables deeper insight into skewness, outliers, and clustering.
Frequently Asked Questions
What if there are multiple modes?
The calculator reports all modes with the highest frequency. If every value is unique, it notes the absence of a mode.
Why show both population and sample variance?
Population variance divides by n, while sample variance divides by n − 1 for unbiased estimation when analyzing samples.
Can I include negative numbers or decimals?
Yes. The calculator accepts any real-valued dataset.
How many data points are required?
You need at least one observation for basic statistics and at least two for sample variance and standard deviation.