Glossary

Statistics and business-metric terms in one place.

Describing data 8

Center, spread and shape of a distribution

Mean→ covered in a lesson: The sum of all values divided by their count. It marks the centre of gravity of the data: if every observation were identical, each one would equal the mean.; $\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i$
Median→ covered in a lesson: The value that splits the ordered list in half: half the observations fall below it, half above. With an even count you take the midpoint of the two central values.
Mode→ covered in a lesson: The value that occurs most often. It is the only measure of centre that works for categories — the best-selling product, the most common payment method.
Variance→ covered in a lesson: The average squared deviation of values from their mean: the more spread out the data, the larger it gets. It is measured in squared original units — dollars², minutes².; $\sigma^2 = \frac{1}{n}\sum (x_i - \bar{x})^2$
Standard deviation (σ)→ covered in a lesson: The square root of the variance: the typical distance from the mean to a single observation, in the same units as the data. For a normal distribution about 68% of values lie within ±1σ of the mean and 95% within ±2σ.; $\sigma = \sqrt{\frac{1}{n}\sum (x_i - \bar{x})^2}$
Percentile / quartile→ covered in a lesson: The value below which a given share of the data lies: p95 is the threshold that 95% of observations do not exceed. Quartiles are the 25th, 50th and 75th percentiles (Q1, median, Q3).
Normal distribution→ covered in a lesson: A symmetric bell-shaped distribution fully described by two numbers: the mean μ (where the peak sits) and the standard deviation σ (how wide the bell is). The 68-95-99.7 rule: ±1σ, ±2σ and ±3σ contain 68%, 95% and 99.7% of values.
Skewness→ covered in a lesson: A measure of asymmetry in a distribution: one tail stretches further than the other. Under right skew, rare large values pull the mean up above the median.

Probability 5

The language of uncertainty and why averages are stable

Probability→ covered in a lesson: A number from 0 to 1 saying how expected an event is: 0 means impossible, 1 means certain. Under the frequentist reading it is the share of cases in which the event occurs if the trial is repeated many times.
Law of large numbers→ covered in a lesson: As trials accumulate, the observed share converges to the true probability. The law describes the behaviour of the average over a long run and says nothing about any individual trial.
Conditional probability→ covered in a lesson: The probability of event A given that event B has already happened, written P(A|B). It differs from the reverse quantity P(B|A) — these are different numbers.; $P(A|B) = \frac{P(A \cap B)}{P(B)}$
Bayes’ theorem→ covered in a lesson: The rule for updating a probability once new data arrives: P(A|B) = P(B|A)·P(A) / P(B). It accounts for the base rate P(A) — how common the event is before any evidence.; $P(A|B) = \frac{P(B|A)\cdot P(A)}{P(B)}$
CLT→ covered in a lesson: The central limit theorem: take samples from almost any distribution and compute the mean of each, and the distribution of those means tends toward normal while its spread shrinks as σ/√n.; $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$

Estimation and hypothesis testing 10

Judging the whole from a sample and reading A/B tests

Standard error→ covered in a lesson: The standard deviation of the estimate itself rather than of the data: how much the mean varies from one sample to another. For a mean, SE = σ/√n.; $SE = \frac{\sigma}{\sqrt{n}}$
Confidence interval→ covered in a lesson: A range of plausible values for the quantity being estimated. The interpretation applies to the method: repeat the experiment many times, build a 95% interval each time, and about 95% of those intervals will cover the true value.; $\bar{x} \pm z \cdot SE$
Bootstrap→ covered in a lesson: Estimating uncertainty without formulas: from the sample you have, repeatedly draw a new sample of the same size with replacement and observe how the statistic of interest varies.
Null hypothesis (H0)→ covered in a lesson: The claim that there is no effect and the observed difference is chance. Testing proceeds by contradiction: you compute how implausible the observed data would be in a world without the effect.
p-value→ covered in a lesson: The probability of seeing a result at least this extreme if there is genuinely no effect. It is not the probability that the hypothesis is true, and it is not the size of the effect.
Type I error (α)→ covered in a lesson: A false positive: the test rejected a true null hypothesis, declaring an effect that does not exist. The level α is chosen in advance and is the share of such errors accepted (usually 0.05).
Type II error (β)→ covered in a lesson: A false negative: the effect is genuinely there but the test failed to detect it. The converse — detecting an effect that exists — is called power and equals 1−β.; $\text{power} = 1 - \beta$
Power→ covered in a lesson: The probability of detecting an effect of a given size, assuming it is genuinely there. It depends on the effect size, the spread of the data, the sample size and the chosen α.; $1 - \beta$
t-test→ covered in a lesson: A test comparing the means of two groups: it measures the observed difference against the standard error of that difference. It assumes independent observations and roughly normal sample means.; $t = \frac{\bar{x}_1 - \bar{x}_2}{SE_{\text{diff}}}$
Multiple comparisons→ covered in a lesson: Testing many hypotheses at once — several metrics, segments or variants. The risk of a false positive accumulates: with 20 independent tests at α=0.05, at least one false "significant" appears about 64% of the time.; $P(\text{at least one error}) = 1 - (1-\alpha)^m$

Relationships and models 5

Relationships between variables and model quality

Correlation (r)→ covered in a lesson: A number from −1 to +1 describing the strength and direction of a linear relationship. Zero means no linear relationship, not the absence of any relationship.
Regression / OLS→ covered in a lesson: A method that fits a line (or a more complex shape) so the sum of squared deviations of the points from it is as small as possible. The slope shows how much y changes on average when x rises by one.; $y = b_0 + b_1 x$
Overfitting→ covered in a lesson: The model learned the random noise of the training data rather than the pattern: excellent results there, poor results on new data. It shows up as a gap between training and hold-out performance.
Precision / Recall→ covered in a lesson: Precision — of the items the model assigned to a class, what share was assigned correctly. Recall — what share of the items actually in that class the model found.; $\text{precision} = \frac{TP}{TP+FP},\quad \text{recall} = \frac{TP}{TP+FN}$
ROC / AUC→ covered in a lesson: The ROC curve shows how the shares of true positives and false positives relate as the classifier threshold is swept across its whole range. AUC is the area under that curve: 1.0 is perfect, 0.5 is coin-flip guessing.

Interpretation traps 3

Where conclusions from data most often break

Simpson’s paradox→ covered in a lesson: A relationship visible in the aggregate reverses inside every subgroup. The cause is a hidden factor distributed unevenly across the groups.
Survivorship bias→ covered in a lesson: A distortion where conclusions are drawn only from the cases that survived into the data, while those that dropped out are invisible.
Goodhart’s law→ covered in a lesson: Once a measure becomes a target, it starts being optimized directly and stops reflecting whatever it was introduced to capture.

Time series and forecasting 9

The structure of a series over time and checking forecasts

Time series→ covered in a lesson: A sequence of metric values ordered in time at a constant step. Neighboring observations depend on each other, so the usual methods built for independent data cannot be applied to a series without caveats.
Trend and seasonality→ covered in a lesson: Two regular components of a series: the trend is slow directional movement, seasonality is oscillation with a known period (day of week, month of year). What remains after removing them is treated as noise.; y = T + S + E
Autocorrelation→ covered in a lesson: The correlation of a series with itself shifted a few steps back. It breaks the assumption of independent observations: standard errors come out too small and confidence intervals narrower than they should be.; $r_k = corr(y_t, y_{t-k})$
Stationarity→ covered in a lesson: The property of a series whose mean, spread and dependence structure do not change over time. Most forecasting models require it: only then does what was learned from the past carry over to the future.
Differencing→ covered in a lesson: Moving from the values of a series to their changes. It removes the trend and makes the series stationary; a seasonal difference (subtracting the value one period earlier) removes the cycle. The I in ARIMA.; $Δy_t = y_t − y_{t−1}$
Exponential smoothing→ covered in a lesson: A forecast from a weighted past, where the weight of observations decays geometrically with age. The Holt-Winters extension keeps level, trend and seasonality as separate components and extends each of them.; $L_t = α·y_t + (1−α)·L_{t−1}$
ARIMA / SARIMA / SARIMAX→ covered in a lesson: A family of models that describe a series through its past: AR is dependence on past values, I is differencing, MA is a correction for past errors. S adds the same mechanisms at the seasonal lag, X adds external features (promos, holidays) whose future values are known in advance.; (p,d,q)(P,D,Q)ₘ
Forecast backtest→ covered in a lesson: Checking a forecast on history: training only on data before a cutoff and comparing with the actuals after it. The cutoff is moved several times, because an evaluation on one split is an evaluation on one observation.
MAE / RMSE / MAPE→ covered in a lesson: Forecast error metrics: MAE is the average miss in the metric's units, RMSE adds a heavier penalty for large misses, MAPE is the error as a percentage of the actual. MAPE is undefined at zero values and asymmetric; for such series MASE is used — the error divided by the error of a naive forecast.; MAE = (1/n)·Σ|y − ŷ|

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Data analytics in plain words: how to count metrics, how not to fool yourself in an A/B test, what gets asked in interviews and how this site gets built. The channel is in Russian.

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