Statistics Calculator - Descriptive Stats, Probability, Hypothesis Testing & Regression Stati...

Statistics Calculator

Descriptive Statistics Calculator

💡 How It Works:
Enter your data values separated by commas, spaces, or new lines. The calculator will compute all major descriptive statistics including central tendency, dispersion, and distribution shape measures.

Enter Data Values 12, 15, 18, 21, 24, 27, 30

Decimal Places 4 decimal places 2 decimal places Whole number

💡 Data Tips:
• Handles negative numbers and decimals
• Ignores non-numeric characters
• Minimum 2 values required for most calculations
• Outliers will affect mean and standard deviation

Probability Calculator

💡 How It Works:
Calculate probabilities for normal distribution. Find probabilities for ranges and visualize the distribution.

Distribution Type Normal Distribution (simplified)

Mean (μ)

Standard Deviation (σ)

Calculation Type P(X < x) P(X > x) P(a < X < b)

Value (x)

Range (a to b)

⚠️ Note: This simplified calculator uses the empirical rule (68-95-99.7) for normal distribution probabilities. For precise calculations, use statistical software.

Hypothesis Testing

💡 How It Works:
Perform one-sample t-test to compare sample mean against a hypothesized population mean.

Test Type One-Sample t-Test (simplified)

Sample Data 22, 25, 28, 31, 34, 37, 40

Hypothesized Mean (μ₀)

Significance Level (α) 0.01 (99% confidence) 0.05 (95% confidence) 0.10 (90% confidence)

⚠️ Note: This simplified calculator provides basic t-test functionality. For comprehensive hypothesis testing with multiple test types, use dedicated statistical software.

Regression Analysis

💡 How It Works:
Perform simple linear regression analysis. Enter paired x and y values to calculate the regression equation, correlation coefficient, and coefficient of determination.

Independent Variable (X) 1, 2, 3, 4, 5, 6, 7

Dependent Variable (Y) 2, 4, 5, 4, 5, 7, 8

Decimal Places 4 decimal places 2 decimal places Whole number

💡 Regression Notes:
• Minimum 3 data points required
• X and Y must have the same number of values
• Correlation coefficient (r) ranges from -1 to 1
• R² represents the proportion of variance explained by the model

Statistical Results

Count (n): 7

Mean (x̄): 21.00

Median: 21.00

Standard Deviation (s): 6.48

Variance (s²): 42.00

Calculation Type: Descriptive Statistics

📋 Step-by-Step Calculation:

1

Parse input data: [12, 15, 18, 21, 24, 27, 30]

2

Count: n = 7 values

3

Mean: (12 + 15 + 18 + 21 + 24 + 27 + 30) / 7 = 147 / 7 = 21.00

4

Median: Middle value when sorted = 21.00

5

Standard Deviation: √[Σ(xᵢ-21.00)²/(7-1)] = √42.00 = 6.48

Data Distribution

21.00

21.00

6.48

42.00

Mean Median Std Dev Variance

💡 Interpretation:
The dataset has a mean of 21.00 and standard deviation of 6.48, indicating moderate variability. The distribution is symmetric (mean = median), suggesting no significant skewness in the data.

Mastering Statistics: From Descriptive Analysis to Inferential Insights

Statistics provides the essential framework for transforming raw data into meaningful insights across scientific research, business analytics, healthcare, and social sciences...

Core Statistical Formulas:

Mean: x̄ = Σxᵢ/n
Standard Deviation: s = √[Σ(xᵢ-x̄)²/(n-1)]
Z-Score: z = (x-μ)/σ
t-Statistic: t = (x̄-μ)/(s/√n)
Correlation: r = Σ[(xᵢ-x̄)(yᵢ-ȳ)]/√[Σ(xᵢ-x̄)²Σ(yᵢ-ȳ)²]
Regression Line: ŷ = a + bx where b = r(s_y/s_x), a = ȳ-bx̄

Frequently Asked Questions About Statistics