Statistics
Statistics for an analyst is not about formulas for their own sake but about not lying to yourself with a number. The mean on skewed data, a metric's "normality", an aggregate that moves opposite to all of its parts — it is easy to draw a confident but wrong conclusion here.
The interview checks exactly this: whether you separate the mean from the median, understand what the CLT actually says, and know why you cannot judge an overall figure from within-group trends. The map below runs from measures of center to Simpson's paradox.
Topic map
- Measures of central tendency — mode, median, and mean, and why the median is robust to outliers.
- Distribution shape and skew — the mode < median < mean order under right skew and where the tail pulls.
- Probability distributions — normal, Poisson, exponential, and others matched to the nature of the variable.
- The central limit theorem — why the distribution of the mean approaches normal and what that gives A/B tests.
- Simpson's paradox — how an aggregate falls even though it rose in every group.
Common traps
| Mistake | Consequence |
|---|---|
| Confusing the mean and median on skewed data | A false picture of the "typical" value |
| Reversing the order of the measures under skew | Describes left skew instead of right |
| Naming measures of spread instead of distributions | An answer off the question |
| Thinking the CLT makes the raw data normal | The sample mean is normal, not the individual values |
| Forgetting the CLT conditions — finite variance, independence | The theorem applied where it does not hold |
| Judging an aggregate from within-group trends | Simpson's paradox — the weight shift is missed |
Interview relevance
Statistics is asked to filter out candidates who compute but do not understand. A strong answer always names the condition and the context — "the median for skewed data", "the CLT is about the distribution of the mean, under finite variance".
Typical checks:
- The difference between mode, median, and mean and robustness to outliers.
- The order of the three measures under skew.
- The exact statement of the CLT and where it applies.
- Whether an aggregate can fall while every group rose (Simpson).
Common wrong answer: "by the CLT any large sample becomes normal". No — the distribution of the sample mean becomes normal, while the data itself may stay arbitrarily skewed.