Statistics Glossary: Essential Statistical Terms for Data Analysts

| Term | Definition | Example | |------|------------|---------| | Mean | Average value (sum ÷ count) | Sales: [100, 200, 300] → Mean = 200 | | Median | Middle value when sorted (50th percentile) | Sales: [100, 200, 10000] → Median = 200 (not affected by outlier 10000) | | Mode | Most frequently occurring value | Ratings: [5,4,5,3,5,4] → Mode = 5 | | Range | Difference between max and min | Prices: [₹50, ₹500] → Range = ₹450 | | Standard Deviation (SD) | Average distance from mean (measures spread) | Low SD = data clustered near mean; High SD = widely spread | | Variance | Standard deviation squared (σ²) | If SD = 10, then variance = 100 | | Percentile | Value below which X% of data falls | 90th percentile salary = ₹12 LPA means 90% earn less than this | | Quartile | Divide data into 4 equal parts | Q1=25th percentile, Q2=median, Q3=75th percentile | | Interquartile Range (IQR) | Q3 - Q1 (middle 50% of data) | Used to detect outliers: values below Q1-1.5×IQR or above Q3+1.5×IQR | | Outlier | Data point far from others | Salary dataset: [₹5L, ₹6L, ₹5.5L, ₹50L] → ₹50L is an outlier | | Distribution | How data values are spread | Normal, skewed, uniform, bimodal | | Skewness | Asymmetry in distribution | Positive skew = tail on right (most salaries low, few very high) |

Learn more about Mean, Median, Mode

| Term | Definition | Example | |------|------------|---------| | Probability | Likelihood of event (0 to 1, or 0% to 100%) | Probability of rain tomorrow = 0.7 (70% chance) | | Sample Space | All possible outcomes | Coin flip: ; Dice roll: | | Event | Specific outcome or set of outcomes | Rolling an even number on a dice: | | Independent Events | One doesn't affect the other | Coin flip 1 doesn't change probability of coin flip 2 | | Dependent Events | One affects the other | Drawing cards without replacement (first draw changes deck) | | Conditional Probability | P(A given B happened) = P(A∣B) | Probability of promotion given you have MBA degree | | Bayes' Theorem | Update probability with new evidence | Used in spam filters (P(spam ∣ word "free" appears)) | | Expected Value | Average outcome if repeated many times | Lottery ticket: -₹10 (you lose on average despite small chance of winning) | | Law of Large Numbers | More trials → results approach true probability | Flip coin 10 times: might get 7 heads; flip 10,000 times → ~50% heads |

| Distribution | Definition | Example Use Case | |--------------|------------|------------------| | Normal Distribution | Bell curve (symmetric, mean=median=mode) | Heights, IQ scores, measurement errors | | Standard Normal (Z) | Normal with mean=0, SD=1 | Used for z-scores to compare across different scales | | Binomial Distribution | Number of successes in n trials (yes/no outcome) | Number of heads in 10 coin flips; conversion rate (click/no click) | | Poisson Distribution | Count of events in fixed time/space | Number of customer arrivals per hour; bugs per 1000 lines of code | | Uniform Distribution | All values equally likely | Random number generator (1-100); ideal dice roll | | Exponential Distribution | Time until next event | Time between customer arrivals; product lifespan | | Chi-Square Distribution | Used in hypothesis tests | Chi-square test for categorical independence | | T-Distribution | Like normal but with heavier tails | Used when sample size is small (<30) |

Learn more about Normal Distribution

| Term | Definition | Example | |------|------------|---------| | Hypothesis | Testable statement about population | "New website design increases conversion rate" | | Null Hypothesis (H₀) | Default assumption (no effect/difference) | H₀: Conversion rate (new) = Conversion rate (old) | | Alternative Hypothesis (H₁) | What you're trying to prove | H₁: Conversion rate (new) > Conversion rate (old) | | P-value | Probability of seeing results if H₀ is true | p=0.03 means 3% chance results are due to luck (not real effect) | | Significance Level (α) | Threshold for rejecting H₀ (usually 0.05) | If p < 0.05, reject H₀ (result is "statistically significant") | | Confidence Level | 1 - α (usually 95%) | 95% confident the effect is real (not due to chance) | | Type I Error | False positive (reject true H₀) | Conclude new design works, but it doesn't (5% chance with α=0.05) | | Type II Error | False negative (fail to reject false H₀) | Conclude no difference, but new design actually is better | | Power | 1 - P(Type II error) | High power (80%+) = good chance of detecting real effect if it exists | | Statistical Significance | p < α (usually p < 0.05) | Result unlikely due to chance alone | | Practical Significance | Effect size large enough to matter | Conversion 2.1% → 2.2% is statistically significant but not practically useful | | Sample Size | Number of observations | Larger sample → more power to detect small effects |

Learn more about P-value | A/B Testing Guide

| Term | Definition | Example | |------|------------|---------| | Confidence Interval (CI) | Range likely to contain true value | 95% CI: [₹5.2L, ₹6.8L] (95% confident true average salary is in this range) | | Margin of Error | Half-width of CI | CI = estimate ± margin of error | | Standard Error (SE) | SD of sampling distribution | SE = SD / √n (larger sample → smaller SE → narrower CI) | | Z-score | # of SDs away from mean | z = (x - mean) / SD; z=2 means 2 SDs above mean | | T-score | Like z-score but for small samples | Used when n < 30 or population SD unknown | | Degrees of Freedom (df) | n - 1 (affects t-distribution shape) | More df → t-distribution closer to normal | | Central Limit Theorem | Sample means → normal as n increases | Even if population is skewed, sample means form bell curve (if n ≥ 30) | | Population | Entire group you want to study | All Flipkart customers (450M) | | Sample | Subset actually measured | Survey 10,000 customers to estimate population average | | Sampling Distribution | Distribution of sample statistics | Distribution of means from many samples | | Bias | Systematic error in one direction | Surveying only iPhone users (excludes Android users) → biased sample | | Random Sample | Every member has equal chance of selection | Ensures sample represents population |

Learn more about Confidence Intervals

| Term | Definition | Example | |------|------------|---------| | Correlation | Strength of linear relationship (-1 to +1) | r=0.8: Strong positive (ad spend ↑ → sales ↑) | | Positive Correlation | Both variables increase together | Study hours ↑ → exam score ↑ | | Negative Correlation | One increases, other decreases | Price ↑ → demand ↓ | | Correlation Coefficient (r) | Pearson's r measures linear correlation | r=1 (perfect positive), r=0 (no correlation), r=-1 (perfect negative) | | Causation | One variable causes the other | Smoking → lung cancer (not just correlated) | | Correlation ≠ Causation | Correlation doesn't prove causation | Ice cream sales correlate with drowning deaths (both caused by summer, not each other) | | Linear Regression | Find best-fit line (y = mx + b) | Predict salary from years of experience | | Slope (m) | Change in y per unit change in x | m=5000: Each year of experience → ₹5000 higher salary | | Intercept (b) | y-value when x=0 | b=₹3L: Starting salary with 0 experience | | R-squared (R²) | % of variance explained by model | R²=0.75: Model explains 75% of salary variation | | Residual | Actual value - predicted value | Actual salary ₹8L, predicted ₹7.5L → residual = ₹0.5L | | Multiple Regression | Predict y from multiple x variables | Predict salary from experience + education + city |

Learn more about Correlation vs Causation