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🧠 Top 10 Statistics Formulas Every Data Analyst Should Know

Why These Formulas Matter Statistics is the foundation of data science, analytics, research, and decision-making. These formulas help you:

Understand and summarize data

Identify patterns and trends

Test hypotheses and assumptions

Communicate insights clearly

Let’s explore the top 10 formulas you must know.

1. Mean (Average)

Formula: Mean = (x₁ + x₂ + ... + xₙ) / n

Explanation: The central value of a dataset — helps in understanding the overall trend.

2. Standard Deviation (σ)

Formula: σ = √[Σ(xᵢ - μ)² / n]

Explanation: Shows how spread out the numbers are from the mean — key for variability.

3. Variance (σ²)

Formula: σ² = Σ(xᵢ - μ)² / n

Explanation: The square of standard deviation — useful in model evaluation and statistics.

4. Probability (P)

Formula: P(A) = Number of favorable outcomes / Total outcomes

Explanation: Core of inferential statistics — used in predictions and risk assessment.

5. Bayes’ Theorem

Formula: P(A|B) = [P(B|A) × P(A)] / P(B)

Explanation: Calculates conditional probability — widely used in ML and diagnostics.

6. Z-Score

Formula: z = (x - μ) / σ

Explanation: Tells how many standard deviations a point is from the mean — useful for anomaly detection.

7. Confidence Interval (CI)

Formula: CI = x̄ ± Z*(σ/√n)

Explanation: Gives a range that likely contains the true population mean — essential for surveys.

8. p-value

Formula: Depends on test statistic (e.g., t or z distribution)

Explanation: Tells the probability of observing results under the null hypothesis — core for significance testing.

9. t-Test Statistic

Formula: t = (x̄₁ - x̄₂) / √[(s₁²/n₁) + (s₂²/n₂)]

Explanation: Used to compare means between two groups — key in A/B testing.

10. Pearson’s Correlation Coefficient (r)

Formula: r = Σ[(x - x̄)(y - ȳ)] / √[Σ(x - x̄)² × Σ(y - ȳ)²]

Explanation: Measures the strength and direction of a linear relationship between two variables.

Final Thoughts These formulas are the backbone of statistical reasoning and data analysis. Whether you’re exploring customer trends, testing experiments, or interpreting research — they’re must-haves.

📌 Save this as your go-to stats cheat sheet.

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