Top 20 Interview Questions on Descriptive and Inferential Statistics

 (Because knowing mean isn’t enough if you can’t explain why it matters)

Let’s be real: you can recite “mean, median, mode” in your sleep.

But in interviews, what separates good candidates from the selected ones is how you explain why stats matter, how you think, and how you’ve used them.

Here are 20 questions people often ask (or should ask) about descriptive & inferential statistics. For each, I’ve included:

• What the interviewer is really looking for?
• What makes for a good answer?
• A mini example or calculation.
• Common mistakes to avoid.

1. What are the measures of central tendency? When would you prefer median over mean?

What they’re testing: Basic understanding + judgement.

Sample answer:
“The most widely used measures of central tendency are mean, median, and mode. Mean is the arithmetic average and works well if your data is symmetric without outliers. But if you have skewed data or big outliers (say salaries or house prices), median is often more robust because it isn’t dragged by extreme values.”

Example:
 Data: [10, 12, 14, 18, 100]

• Mean = (10 + 12 + 14 + 18 + 100)/5 = 30.8
• Median = 14

Here, median (14) better represents the “central” than mean (30.8).

Common mistake: Saying “mean is always better” or “median is always used for skewed data” without explaining why.

2. What is dispersion or variability? Name a few measures and when you use each.

What they’re testing: Depth beyond “just variance.”

Sample answer:
 “Dispersion shows how data spreads around central tendency. Key measures: range (max−min), interquartile range (IQR), variance, standard deviation.

If I want robustness (less influenced by outliers), I prefer IQR or median absolute deviation; whereas for normal distributions, standard deviation and variance can give more insight.”

Example:
Dataset A: [5,5,5,5,5] → Range = 0; Data B: [2,5,8,12,20] → Range = 18.

Common mistake: Using range alone as dispersion in skewed data, or forgetting that variance is in squared units (makes interpretation harder).

3. Explain variance vs standard deviation. Why do we take square root for SD?

What they’re testing: Mathematical understanding + interpretation.

Good answer:
 “Variance measures average squared deviations from the mean. Standard deviation is its square root, which brings the units back to the original scale. Without taking the square root, variance is harder to interpret (squared units).

SD helps us answer “on average, how far away is a data point from the mean?””

Mini example:
Data: [2,4,6] → mean = 4

• Variance = ((2‑4)² + (4‑4)² + (6‑4)²)/3 = (4 + 0 + 4)/3 ≈ 2.67
• SD = √2.67 ≈ 1.63

Common mistake: Forgetting population vs sample formulas (division by N vs N‑1).

4. What is skewness and kurtosis? How do they affect your interpretation?

What they’re testing: Knowledge of shape of distribution.

Good answer:
 “Skewness tells us about asymmetry: whether the tail is longer on the left or right. Positive skew means the tail is on the right.

Kurtosis, on the other hand, measures how “heavy” or “light” tails are compared to a normal distribution. In simple terms, high kurtosis = more outliers. They help me understand if my assumption of normality holds, or whether I need transformations.”

Common mistake: Saying skewness >0 is “bad” without context, or confusing kurtosis with peakedness only.

5. What are quartiles and how is IQR calculated? Why is IQR useful?

What they’re testing: Robust descriptive stats tools.

Sample answer:
 “Quartiles divide data into 4 parts. Q1 (25th percentile), Q2 (median), Q3 (75th percentile).

Interquartile range is represented as IQR, which is basically the difference between third and first quartile (IQR= Q3 − Q1). This basically gives the middle 50% spread.

Advantages: ignores extremes; good for skewed distributions and detecting outliers.”

Example:
 Data sorted: [1,3,7,8,9,12,15] → Q1 ≈ 3, Q3 = 12 → IQR = 12−3 = 9.

6. What are confidence intervals? What do they really mean?

What they’re testing: Understanding uncertainty and inference.

Sample answer:
“A confidence interval gives a range in which we believe the true parameter (like a population mean) lies with a certain confidence (say 95%).

It also captures sampling variability; i.e., if we repeated the study many times, 95% of intervals would contain the true value.”

Mini calculation:
Suppose sample mean = 50, sample size = 100, sample SD = 10. For 95% CI: around mean ± (1.96 * SD/√n) = 50 ± (1.96 *10/10) = 50 ± 1.96 → CI ~ [48.04, 51.96].

Common mistake: Saying “there’s a 95% chance the true mean is in this interval” (that’s wrong wording for frequentist CIs).

7. Explain the difference between population parameter vs sample statistic.

What they’re testing: Foundations of inferential stats.

Sample answer:
 “A parameter is a fixed number describing population (e.g., true mean of all customers).

A statistic is computed from sample (e.g., sample mean) to estimate the parameter.

Because we can’t observe full populations often, we rely on statistics and measure their accuracy via sampling error.”

8. What is margin of error? How does sample size affect it?

What they’re testing: Trade‑offs between precision, cost, data size.

Sample answer:
 “Margin of error shows how precise your estimate is, tied to confidence level and standard error.

Larger sample size → smaller standard error → smaller margin of error. Also, more variability in data increases margin of error.”

9. What is point estimation vs interval estimation?

What they’re testing: Understanding of estimation methods.

Sample answer:
“Point estimation gives a single best guess (like sample mean). Interval estimation, on the other hand, gives a range (like CI) that captures uncertainty.

Interviewers want to know both: ‘What is your guess?’ + ‘How sure are you?’”

10. What are unbiased estimator and efficient estimator?

What they’re testing: Properties of good estimators.

Sample answer:
 “An estimator is unbiased if its expected value equals the true parameter. Efficient means among unbiased estimators, it has the smallest variance.

For example, sample mean is unbiased estimator of population mean, and often efficient under normal assumptions.”

11. When would you use a t‑distribution instead of z‑distribution?

What they’re testing: Use situations, sample size, when variance is unknown.

Sample answer:
 “When population variance is unknown and/or sample size small (usually 0), we use t‑distribution. It has heavier tails to reflect greater uncertainty. As n → large, t distro approximates z.”

12. What is a null hypothesis? What are type I and type II errors?

What they’re testing: Hypothesis testing basics.

Sample answer:
 “Null hypothesis is the default assumption (e.g., that there is no effect).

Type I error = rejecting null when it is true (false positive).

Type II error = failing to reject null when it’s false (false negative).

Depending on the business need, you may want to minimize one over the other.”

13. What does p‑value < 0.05 mean? Is that always significant?

What they’re testing: Misinterpretation, nuance.

Sample answer:
 “p < 0.05 means that if the null hypothesis were true, observing the data (or more extreme) has less than 5% probability. It’s a convention, not a magic cut‑off. Statistical significance doesn’t always mean practical significance.”

14. Explain the Central Limit Theorem (CLT). Why is it useful?

What they’re testing: Key inferential concept.

Good answer:
 “CLT says that the sampling distribution of the sample mean tends to normal distribution as the sample size increases, regardless of population distribution (if variance finite). This allows us to use z/t methods even when population isn’t normal, provided sample size is large enough.”

15. What is the difference between parametric vs non‑parametric methods?

What they’re testing: Method choice, assumptions.

Good answer:
 “Parametric methods assume a specific distribution (e.g., normal). Non‑parametric make fewer assumptions (e.g., median test, bootstrap). If you’re unsure about underlying distribution or have small data, non‑parametric is safer.”

16. What is bootstrapping? When do you use it?

What they’re testing: Modern inferential tools.

Good answer:
 “Bootstrapping is resampling with replacement to approximate the sampling distribution of a statistic. Useful when theoretical distribution are unknown or the sample size is small. For example, estimating CI of median via bootstrap.”

17. What is power of a test? Why is it important?

What they’re testing: Sensitivity and reliability.

Good answer:
 “Power of a test represents the probability of correctly rejecting the null hypothesis when it is false (1 ‑ type II error). A test with low power might miss real effects. In practice, we calculate required sample sizes to achieve desired power (80% or 90%).”

18. What is ANOVA? When do you use it?

What they’re testing: Comparing more than two groups.

Good answer:
 “ANOVA (Analysis of Variance) allows comparing means across more than two groups while controlling Type I error rate. If you compare 3 or more groups, instead of doing multiple t‑tests (which inflates error), use ANOVA.”

19. What is hypothesis testing for proportions?

What they’re testing: Working with binary/categorical outcomes.

Good answer:
 “You compare observed proportion to expected; uses z‑test for large samples or exact methods when sample small. For example, checking if click‑through rate differs from 5%. Must check conditions (np, n(1‑p) large enough).”

20. What is multiple testing / correction (Bonferroni, FDR)? Why does it matter?

What they’re testing: Awareness of pitfalls in inference.

Good answer:
 “When you run many hypothesis tests, chance of false positives increases. Bonferroni correction divides alpha by #tests; False Discovery Rate (e.g., Benjamini‑Hochberg) offers a trade‑off between discovering true effects and limiting false ones. Important in fields like genomics or A/B tests with many variants.”

Bonus tips to nail these questions

• Always answer with a mini example or calculation if you can.
• Clarify assumptions (e.g., sample size, distribution).
• Don’t just define — talk about when you’d use this in real projects.
• Be honest about limitations. Interviewers respect nuance.

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