🎓 Mathematics • Statistics
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Statistics Calculator
Full descriptive statistics solver computing mean, sample/population variance, standard deviation, and IQR.
Studio-Grade Mathematical Suite
Math & Statistics Calculator
High-precision percentage, fraction arithmetic, ratio scaling, dataset averages, statistical variance, and combinatorics.
Sample Datasets:
Sample Std Dev (s)
26.4281
Population Std Dev (σ)
Sample Variance (s²)
698.447
Interquartile Range (IQR)
39.5
Count (N): 12
Sum: 605
Min: 12
Max: 92
Q1:
Q3:
What is Descriptive Statistics?
Descriptive statistics summarize and describe characteristics of a dataset without drawing conclusions beyond the data.
Variance and standard deviation quantify the degree of dispersion or spread around the mean.
Formula & Step-by-Step Calculation
s = √[ ∑(xᵢ - x̄)² / (n - 1) ], σ = √[ ∑(xᵢ - μ)² / N ]
Formulas for sample standard deviation s and population standard deviation σ.
Worked Step-by-Step Examples
Example 1
Find std dev of 2, 4, 4, 4, 5, 5, 7, 9
Solution: s = 2.14
• Mean = 5, SS = 32, Variance = 32/7 ≈ 4.57, Std Dev = √4.57 ≈ 2.14
Common Real-World & Academic Use Cases
- ✓ Scientific experimental error analysis
- ✓ Financial portfolio risk volatility (Beta)
- ✓ Quality control tolerances
How to Use the Statistics Calculator
1
Enter Numbers
Paste or type dataset separated by commas.
2
Inspect Metrics
Review sample vs population variance, std dev, and IQR.
Frequently Asked Questions
Q: Why divide by (n - 1) for sample variance?
Bessel’s correction compensates for bias when estimating population variance from a sample.