Statistics Calculator

Calculate statistical measures including mean, median, mode, standard deviation, and probability. Analyze data sets and distributions.

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Statistics Calculator

Comprehensive statistical analysis including descriptive statistics, correlation, regression, hypothesis testing, and distribution analysis

Analysis Type

Data Input

Enter numbers separated by commas (e.g., 1, 2, 3, 4, 5)

📊 Sample Datasets

🧮 Key Formulas

Mean: x̄ = Σx / n
Std Dev: s = √(Σ(x-x̄)² / (n-1))
Correlation: r = Σ(x-x̄)(y-ȳ) / √(Σ(x-x̄)²Σ(y-ȳ)²)
t-test: t = (x̄-μ) / (s/√n)

Descriptive Statistics

Mean

11

Median

11

Std Dev

6.0553

Count

10

Min

2

Max

20

Range

18

Q1

6.5

Q3

15.5

Skewness

0

Normal

Kurtosis

-1.2

Mesokurtic

Data Quality: Good

Completeness: 1.0%

Step-by-Step Analysis

1Data: [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] (n = 10)
2Mean (μ): Sum of all values / n = 11.0000
3Median: Middle value when sorted = 11.0000
4Standard deviation (σ): √(Σ(x-μ)²/(n-1)) = 6.0553
5Range: Max - Min = 20 - 2 = 18
6Quartiles: Q1 = 6.50, Q3 = 15.50, IQR = 9.00

1Mastering Statistics Calculations

Calculate statistical measures including mean, median, mode, and distribution. Whether you're a student, educator, or professional, understanding the mathematical principles behind statistics will enhance your problem-solving abilities. This guide breaks down complex concepts into understandable components and provides practical applications for real-world scenarios.

Mathematical Foundations

The underlying mathematics involves fundamental principles that have wide-ranging applications. Understanding these concepts helps you: • Verify calculator results manually • Apply knowledge to related problems • Develop mathematical intuition • Solve more complex variations • Teach others effectively

Step-by-Step Problem Solving

Approach problems systematically: 1. Identify what you're solving for 2. Gather all necessary information 3. Choose the appropriate formula 4. Perform calculations carefully 5. Verify results make sense 6. Consider alternative methods


2Real-World Applications

Mathematical concepts aren't just theoretical - they have practical applications in many fields.

Professional Applications

Professionals in various fields use these calculations: • Engineers for design and analysis • Scientists for research and experiments • Financial analysts for modeling • Architects for planning and construction • Data scientists for analysis and predictions

Educational Value

For students and educators: • Builds foundational math skills • Develops logical thinking • Prepares for advanced topics • Provides exam preparation • Enables peer tutoring and collaboration

This comprehensive guide is regularly updated to ensure accuracy. Last reviewed: 7/25/2025

Frequently Asked Questions

When should I use mean vs median?

Use mean for normally distributed data, median for skewed data or when outliers are present. Median is less affected by extreme values.

What does standard deviation tell me?

Standard deviation measures data spread around the mean. Low values indicate data points cluster near the mean; high values show more variation.

How do I interpret confidence intervals?

A 95% confidence interval means if you repeated the study 100 times, 95 intervals would contain the true population parameter.