Post by @datascibykashi

Save this. Bookmark it. Come back when you’re doing EDA, building ML models, or preparing for interviews. 🔖 📌 DESCRIPTIVE STATISTICS 1️⃣ Mean [ \bar{x}=\frac{\sum x_i}{n} ] 2️⃣ Weighted Mean [ \bar{x}_w=\frac{\sum w_i x_i}{\sum w_i} ] 3️⃣ Median Middle value after sorting the data. 4️⃣ Mode Most frequently occurring value. 5️⃣ Range [ R=X_{\max}-X_{\min} ] 6️⃣ Population Variance [ \sigma^2=\frac{\sum(x_i-\mu)^2}{N} ] 7️⃣ Sample Variance [ s^2=\frac{\sum(x_i-\bar{x})^2}{n-1} ] 8️⃣ Population Standard Deviation [ \sigma=\sqrt{\sigma^2} ] 9️⃣ Sample Standard Deviation [ s=\sqrt{s^2} ] 🔟 Coefficient of Variation [ CV=\frac{\sigma}{\mu}\times100 ] 📈 POSITION & DISPERSION 1️⃣1️⃣ Percentile Position [ P_k=\frac{k(n+1)}{100} ] 1️⃣2️⃣ Interquartile Range [ IQR=Q_3-Q_1 ] 1️⃣3️⃣ Quartile Deviation [ QD=\frac{Q_3-Q_1}{2} ] 1️⃣4️⃣ Z-Score [ z=\frac{x-\mu}{\sigma} ] 1️⃣5️⃣ Mean Absolute Deviation [ MAD=\frac{\sum|x_i-\bar{x}|}{n} ] 🎲 PROBABILITY 1️⃣6️⃣ Probability [ P(A)=\frac{\text{favorable outcomes}}{\text{total outcomes}} ] 1️⃣7️⃣ Complement Rule [ P(A^c)=1-P(A) ] 1️⃣8️⃣ Addition Rule [ P(A\cup B)=P(A)+P(B)-P(A\cap B) ] 1️⃣9️⃣ Conditional Probability [ P(A|B)=\frac{P(A\cap B)}{P(B)} ] 2️⃣0️⃣ Multiplication Rule [ P(A\cap B)=P(A|B)P(B) ] 📊 DISTRIBUTIONS 2️⃣1️⃣ Binomial Probability [ P(X=k)=\binom nkp^k(1-p)^{n-k} ] 2️⃣2️⃣ Expected Value [ E(X)=\sum xP(x) ] 2️⃣3️⃣ Variance of Random Variable [ Var(X)=E(X^2)-[E(X)]^2 ] 2️⃣4️⃣ Standard Error of Mean [ SE=\frac{\sigma}{\sqrt n} ] 2️⃣5️⃣ Normal Distribution [ f(x)=\frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}} ] 🔗 CORRELATION 2️⃣6️⃣ Covariance [ Cov(X,Y)=\frac{\sum(x_i-\bar{x})(y_i-\bar{y})}{n-1} ] 2️⃣7️⃣ Pearson Correlation [ r=\frac{Cov(X,Y)}{s_Xs_Y} ] 2️⃣8️⃣ Correlation Range [ -1\le r\le1 ] 2️⃣9️⃣ Coefficient of Determination [ R^2=1-\frac{SS_{res}}{SS_{tot}} ] 📉 REGRESSION 3️⃣0️⃣ Simple Linear Regression [ y=\beta_0+\beta_1x+\epsilon ] 3️⃣1️⃣ Slope [ \beta_1=\frac{Cov(X,Y)}{Var(X)} ] 3️⃣2️⃣ Intercept [ \beta_0=\bar{y}-\beta_1\bar{x} ] 3️⃣3️⃣ Residual [ e_i=y_i-\hat{y}_i ] 3️⃣4️⃣ Mean Squared Error [ MSE=\frac{1}{n}\sum(y_i-\hat{y}_i)^2 ] 3️⃣5️⃣ Root Mean Squared Error [ RMSE=\sqrt{MSE} ] 3️⃣6️⃣ Mean Absolute Error [ MAE=\frac{1}{n}\sum|y_i-\hat{y}_i| ] 🧪 HYPOTHESIS TESTING 3️⃣7️⃣ Null Hypothesis [ H_0 ] 3️⃣8️⃣ Alternative Hypothesis [ H_1 ] 3️⃣9️⃣ Z-Test Statistic [ z=\frac{\bar{x}-\mu_0}{\sigma/\sqrt n} ] 4️⃣0️⃣ T-Test Statistic [ t=\frac{\bar{x}-\mu_0}{s/\sqrt n} ] 4️⃣1️⃣ Chi-Square Statistic [ \chi^2=\sum\frac{(O-E)^2}{E} ] 4️⃣2️⃣ F-Statistic [ F=\frac{s_1^2}{s_2^2} ] 4️⃣3️⃣ P-Value Probability of observing results at least as extreme as the observed result, assuming (H_0) is true. 📐 CONFIDENCE & SAMPLING 4️⃣4️⃣ Confidence Interval for Mean [ \bar{x}\pm z_{\alpha/2}\frac{\sigma}{\sqrt n} ] 4️⃣5️⃣ Margin of Error [ ME=z_{\alpha/2}\frac{\sigma}{\sqrt n} ] 4️⃣6️⃣ Sample Size for Mean [ n=\left(\frac{z_{\alpha/2}\sigma}{E}\right)^2 ] 4️⃣7️⃣ Standard Error of Proportion [ SE=\sqrt{\frac{p(1-p)}{n}} ] 🤖 DATA SCIENCE METRICS 4️⃣8️⃣ Accuracy [ Accuracy=\frac{TP+TN}{TP+TN+FP+FN} ] 4️⃣9️⃣ Precision [ Precision=\frac{TP}{TP+FP} ] 5️⃣0️⃣ Recall / Sensitivity [ Recall=\frac{TP}{TP+FN} ] 🚀 THE BIG PICTURE Statistics → EDA → Probability → Hypothesis Testing → Correlation → Regression → Machine Learning You don’t need to memorize every formula blindly. Understand what the formula measures, when to use it, and what the result means. That’s where statistics becomes useful in real-world Data Analytics & Data Science. 📊🔥 🔖 Save this cheat sheet for your next project or interview. #Statistics #DataAnalytics #DataScience #creatorsearchinsights #datascience