Statistics/Data Analytics Interview Questions

Data Characteristics:

• Mean > Median → Right-skewed distribution
• A small number of high-value purchasers pull up the mean
• Most customers purchase $80 or less

Metric Selection:

• Representative value: Recommended to use median ($80)
• For reporting: Express as “Half of customers purchase $80 or less”
• For revenue forecasting: Use mean (related to total sum)

Additional Analysis:

# Check skewness
from scipy import stats
skewness = stats.skew(df['amount'])
print(f"Skewness: {skewness:.2f}")  # Positive means right-skewed
 
# Check quantiles
print(df['amount'].quantile([0.25, 0.5, 0.75, 0.9, 0.99]))

Interviewer Point:

“When should you use the mean?” → Normal distribution, metrics related to total sum

❌ Incorrect Interpretations:

• “There’s a 3% probability the effect exists”
• “There’s a 3% probability the null hypothesis is true”

✅ Correct Interpretation:

“If the null hypothesis is true, the probability of observing the current result (or more extreme results) is 3%”

Simple Explanation:

• “If there really is no effect, this result would only occur 3 times out of 100”
• “Since this is a rare result to be coincidence, we conclude there is an effect”

Limitations of p-value:

1. Does not tell us the size of the effect
2. Small differences become significant with large sample sizes
3. The 0.05 threshold is arbitrary

Interviewer Point:

“What if p-value is 0.051, does that mean there’s no effect?” → Boundary value issue, consider effect size together

Definitions:

• Type I Error (α): Concluding there’s an effect when there isn’t (False Positive)
• Type II Error (β): Concluding there’s no effect when there is (False Negative)

Drug Testing:

• Type I Error: Approving an ineffective drug → Patient harm (more serious)
• Type II Error: Rejecting an effective drug → Opportunity cost

Opposite Case - Spam Filter:

• Type I Error: Marking normal email as spam → Missing important emails (more serious)
• Type II Error: Marking spam as normal → Minor inconvenience

Trade-off:

α ↓ (conservative) → β ↑
α ↑ (aggressive) → β ↓

Business Application:

• Medical/Safety: Minimize Type I error (α = 0.01)
• Marketing tests: Consider Type II error (power ≥ 80%)

Interviewer Point:

“What is statistical power?” → 1 - β, the probability of detecting a real effect