Practice — Descriptive Statistics & Exploratory Data Analysis (6 questions)

Session durations (minutes) for 12 users of a mobile app:

1, 1, 2, 2, 3, 3, 4, 5, 6, 8, 45, 120

A product manager wants "the average session length" for a board slide.

1. Compute the mean and the median. Which would you put on the slide, and how would you phrase it?
2. The finance team separately asks for total minutes of engagement per 1,000 users to size a server bill. Which statistic do they need, and why is it a different answer?
3. Two weeks later the 120-minute session is discovered to be a user who left the app open overnight. Recompute both statistics without it. What does the change tell you about each measure?

A colleague flags outliers in a transaction-amount column using |z| > 3 and reports "no outliers found". You look at the data:

8, 9, 10, 10, 11, 12, 12, 13, 14, 15, 15, 16, 18, 20, 350

1. Compute the z-score of the 350 value (use the sample standard deviation) and explain why the colleague's rule missed it.
2. Apply the IQR rule (use Q_1 = 10, Q_3 = 15.5) and the MAD-based robust z-score. Do they flag 350?
3. The row turns out to be a genuine bulk order from a business customer. Describe two different analyses in which you would handle this row differently, and what "handling" would mean in each.

A survey dataset of 20,000 customers has three columns with missing values:

• household_income: 28% missing. Missingness is 45% among customers aged 55+, 12% among under-35s.
• satisfaction_score: 9% missing. Missing rows are concentrated among customers who later churned.
• device_os: 1.5% missing, uniformly across every segment you check; the collection library had a known intermittent bug that month.

1. Classify each column's likely mechanism (MCAR / MAR / MNAR) and justify.
2. For each, state what naive listwise deletion (dropping any row with a missing value) would do to an analysis of the relationship between income and satisfaction.
3. Propose a handling strategy for each column, including whether a missing indicator is worth adding.

Two onboarding tutorials were live for a month. Completion counts:

1. Compute the completion rate for each tutorial within each segment, and overall. What do you observe?
2. Explain mechanically why the pooled comparison disagrees with the segment comparisons. What is the confounder?
3. Which tutorial would you recommend, and what would you say to a stakeholder who insists "the overall number is what matters"? What would you check in the data before finalising the recommendation?

You receive a table of 120,000 loan applications for a default-prediction project. In your first EDA pass you notice:

• application_id has 118,400 unique values.
• annual_income has a histogram with two clear peaks, roughly at 50,000 and at 50,000,000.
• employment_length contains values "5", "5 years", "5+", "<1", and blanks.
• days_past_due_max has a Pearson correlation of 0.91 with the target defaulted.
• 3% of application_date values are in the year 1970.

1. For each observation, state the most likely cause and the check you would run to confirm it.
2. Which of these could silently produce a model that looks excellent in validation and fails in production? Explain the mechanism.
3. Write down the fix (or decision) for each, in the order you would apply them, and note anything you would document for the team.

For each analytical question, name the plot you would produce first, explain what feature of the data it would reveal that a summary statistic would hide, and name one pitfall of that plot.

1. "Is our API latency worse in the EU region than in the US region?" (2 million requests, timestamped, with region.)
2. "Do users with more support tickets spend more?" (50,000 users; tickets is a small integer 0–15; spend is dollars.)
3. "Which of these 40 numeric features are redundant with each other?"
4. "Has the average order value changed since the pricing update?"
5. What plot would you avoid for question 1, and why?