Data Scientist · #038 · August 30, 2026 · 2 min read
Which statistics concepts do data interviews assume?
Center, spread, outliers, correlation, hypothesis testing and the rules of thumb: the statistics vocabulary every data interview assumes you have, phrased the way you would say it out loud.
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Every data interview assumes this vocabulary, and most candidates can compute the numbers but cannot say what they mean out loud. This page phrases each concept the way you would actually say it. The print-ready A4 PDF is at the bottom.
Center
mean = Σx / n: pulled by outliers.median: the middle value, robust.mode: most frequent.
Spread
std σ: average distance to the mean.IQR = Q3 - Q1: the middle 50%.range = max - min: fragile, one outlier owns it.
Outliers
z = (x - μ) / σ: |z| > 3 is suspicious.x < Q1 - 1.5·IQR: the boxplot fence.log(x): tames right skew before modeling.
Relationships
r ∈ [-1, 1]: direction and strength of a linear relationship.r²: share of variance explained.r = 0.9: still not causation.
Testing
H₀: assume no effect, then try to embarrass that assumption.p-value: P(data this extreme | H₀ true). Nothing more.α = 0.05: your false-alarm budget, chosen before the test.95% CI: the plausible range for the true value.
Rules of thumb
n ≥ 30: where the central limit theorem starts helping.±1σ ≈ 68%,±2σ ≈ 95%: normal-distribution quick math.- mean far from median: the data is skewed, plot it.
The whole sheet, in pandas
x = df["revenue"]
x.mean(), x.median(), x.std()
q1, q3 = x.quantile([.25, .75])
fence = q1 - 1.5 * (q3 - q1)
z = (x - x.mean()) / x.std()
outliers = x[z.abs() > 3]
df[["ads", "revenue"]].corr()
Two minutes, every dataset, before trusting any chart.
The trap: what a p-value is not
| p = 0.03 means | Verdict |
|---|---|
| 3% chance of data this extreme if there is truly no effect | correct |
| "97% chance our hypothesis is right" | wrong |
| "the effect is big enough to matter" | wrong: that is effect size |
And checking the test every day until it dips under 0.05 is called peeking: it manufactures significance out of noise.
Frequently asked questions
What does a p-value actually mean?
The probability of seeing data at least this extreme IF the null hypothesis were true. p = 0.03 means: in a world with no real effect, data like yours shows up 3% of the time. It is not the probability that you are right, and it says nothing about how big the effect is.
When should I use the median instead of the mean?
Whenever the data can be skewed by a few extreme values: salaries, revenues, delays, anything with a long tail. The mean gets pulled by outliers, the median does not. If mean and median are far apart, that gap itself is telling you the distribution is skewed.
How do I detect outliers?
Two standard fences: the z-score, (x minus mean) / std, where |z| > 3 is suspicious; and the boxplot rule, anything below Q1 - 1.5 IQR or above Q3 + 1.5 IQR. Flag first, inspect before deleting: outliers are sometimes the most valuable rows in the table.
Does a high correlation mean one variable causes the other?
No. r = 0.9 says the two move together, nothing more. A third variable can drive both (ice cream sales and drownings both follow summer), or the causality can run backwards. Correlation selects candidates for a causal question; experiments answer it.
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