Statistical Analysis

Mathematical Principles & Theorems

Comprehensive descriptive and inferential statistics: Mean \(\bar{x} = \frac{1}{n}\sum x_i\), Sample Variance \(s^2 = \frac{1}{n-1}\sum (x_i - \bar{x})^2\), Standard Deviation \(s\), Standard Error \(SE = s/\sqrt{n}\). Five-number summary: Min, \(Q_1\), Median \(Q_2\), \(Q_3\), Max with Interquartile Range \(IQR = Q_3 - Q_1\). Ordinary Least Squares (OLS) Linear Regression \(y = \beta_0 + \beta_1 x\) with slope \(\beta_1 = \frac{\text{Cov}(x,y)}{\text{Var}(x)}\) and Pearson correlation coefficient \(r = \frac{\text{Cov}(x,y)}{s_x s_y}\).

Operating Instructions

• Enter numerical datasets (1D series or paired 2D coordinates) into the data textarea.
• Click Analyze to compute complete descriptive statistics (Mean, Median, Std Dev, Skewness, Kurtosis).
• Inspect the interactive histogram, box-and-whisker plot, and normal probability overlay.
• For paired data: View the scatter plot with fitted OLS regression line and coefficient of determination \(R^2\).