Practical Interpretation

Who this is for

Data Analysts who can compute stats (mean, median, percentiles, variance) and want to turn numbers into actionable statements that influence decisions.

Prerequisites

• Comfort computing mean, median, mode, percentiles, variance, and standard deviation.
• Basic familiarity with distributions (skew, outliers).
• Ability to read simple charts (histogram, box plot), even if you do them by hand.

Why this matters

Stakeholders rarely ask for a mean. They ask: “Are most customers happy?” “Will we hit our SLA?” “Which team performs better?” Practical interpretation turns descriptive stats into clear, defensible answers you can explain in one or two sentences.

• Product: Translate rating distributions into a go/no-go for a launch.
• Operations: Turn response time percentiles into SLA statements for support.
• Marketing: Compare campaign performance using center and spread, not just averages.
• Finance: Explain revenue volatility, not just total revenue.

Concept explained simply

Descriptive statistics summarize “what’s typical” and “how much it varies.” Practical interpretation adds: “so what should we do?”

• Center (median or mean): what a typical user experiences.
• Spread (IQR, standard deviation): how consistent the experience is.
• Shape (skew/outliers): whether extremes distort the average.
• Percentiles (P90, P95): the worst-case experience for most people.
• Context: units, segment, time period, sample size, and business target.

Mental model: SCS + Target

Open the mental model

1. Shape: Is it symmetric, right-skewed, left-skewed? Any outliers?
2. Center: Median for skewed data; mean for symmetric data or when every value matters equally.
3. Spread: IQR for robustness; standard deviation for overall variability.
4. Target: Compare stats to a threshold, SLA, or baseline. Turn the comparison into a decision.

One-sentence template: “Typical [unit] is X (median), 90% are within Y (P90); distribution is [shape]. This meets/doesn’t meet [target], so we should [action].”

How to interpret core stats (quick steps)

1. State the question and unit (minutes, dollars, sessions).
2. Check sample size and time window.
3. Scan for skew/outliers (box plot logic or a quick sort).
4. Pick center metric (median for skew; mean for symmetric or budgetary totals).
5. Add a percentile (P90/P95) for “worst-case typical.”
6. Report spread (IQR or SD) when consistency matters.
7. Compare to target and recommend next action.

Worked examples

Example 1 — Support response times (minutes)

Data: [2, 3, 3, 4, 5, 6, 7, 8, 9, 12, 15, 30] (n=12)

• Mean ≈ 8.7 (influenced by 30)
• Median = (6th+7th)/2 = (6+7)/2 = 6.5
• P90: rank = ceil(0.90*12) = 11 → 11th value = 15
• Right-skewed due to the 30-minute outlier

Interpretation: “Typical response is about 6.5 minutes; 90% of tickets get a response within 15 minutes. Right-skewed due to rare long waits.”

Decision: If SLA is P90 under 20 minutes, we’re meeting it; focus on reducing extreme cases.

Example 2 — Daily sales per store (units)

Data: [10, 11, 11, 12, 12, 12, 13, 13, 50] (n=9)

• Mean = 144/9 = 16 (pulled up by 50)
• Median = 12
• Q1 ≈ 11, Q3 ≈ 13 → IQR ≈ 2; outlier rule: Q3+1.5*IQR = 16 → 50 is an outlier

Interpretation: “Most stores sell ~12 units/day; one outlier store skews the mean to 16.”

Decision: Use median to set expectations; separately analyze the outlier to capture best practices.

Example 3 — Product ratings (1–5 stars)

Data: [4.6, 4.7, 4.5, 4.8, 4.9, 4.6, 2.0] (n=7)

• Mean ≈ 4.3, Median = 4.6
• Right tail at low rating (2.0) indicates an incident or subgroup issue

Interpretation: “Typical rating is ~4.6, but there’s a rare low-score cluster pulling the mean down.”

Decision: Keep the headline as median 4.6; investigate the 2.0 case for root cause.

Interpretation checklist

• Stated the unit and time window.
• Picked median/mean appropriately given skew.
• Included a percentile for reliability (P90 or P95).
• Mentioned spread (IQR/SD) if consistency matters.
• Flagged outliers instead of letting them distort the narrative.
• Compared to a clear target or baseline.
• Ended with one actionable recommendation.

Exercises (hands-on)

These mirror the exercises below. Use pen-and-paper or a spreadsheet. Then open the solutions to self-check.

Exercise 1 — Delivery times (days)

Data: [1, 1, 2, 2, 2, 3, 3, 3, 4, 6, 7, 10]

• Tasks: Compute median, mean, Q1, Q3, IQR, and P90. Write a one-sentence customer-facing statement.
• Decision: What promise can the business safely make on the website?

Show solution

Median = 3; Mean = 44/12 ≈ 3.67; Q1 = 2; Q3 = 5; IQR = 3; P90 rank = ceil(0.9*12)=11 → 7.

Interpretation: “Typical delivery is 3 days; 90% arrive within 7 days; a few take up to 10.”

Decision: Promise “Most orders arrive in ~3 days; 90% within a week.”

Exercise 2 — Support teams A vs B (minutes)

Team A: [4, 5, 5, 6, 6, 7, 8, 15]; Team B: [6, 6, 6, 6, 6, 6, 6, 6]

• Tasks: Compute mean, median, and P95 for each. Decide which team better meets an SLA: P95 ≤ 10 minutes and mean ≤ 6.5 minutes.

Show solution

A: Mean = 56/8 = 7; Median = (6+6)/2 = 6; P95 rank = ceil(0.95*8)=8 → 15.

B: Mean = 6; Median = 6; P95 = 6.

Interpretation: Both have similar medians; A has worse tail (15) and higher mean. B meets both SLA criteria; A fails P95 and mean.

Decision: Shift volume to B for critical tickets; coach A to reduce long tails.

Common mistakes and self-checks

• Mistake: Reporting mean on skewed data without noting outliers. Self-check: Compare mean vs median; if far apart, explain why.
• Mistake: Ignoring units/timeframe. Self-check: Can a reader know “how many, how long, when” from your sentence?
• Mistake: Using a single metric. Self-check: Add a percentile to show reliability.
• Mistake: Confusing variability sources. Self-check: Segment by key drivers (channel, region, device) before concluding.
• Mistake: Overprecision. Self-check: Round to decision-ready numbers (e.g., “~6.5 minutes”).
• Mistake: No action. Self-check: End with a recommendation tied to a target.

Practical projects

• Support SLA brief: Analyze 4 weeks of response times. Produce one slide with median, P90, and a yes/no on SLA, plus one action.
• Store performance snapshot: Use median vs mean sales per store; flag outliers; write a 3-line summary for managers.
• Ratings quality check: Compare median rating by version/region; propose a fix for the worst tail.

Learning path

• Before this: Compute descriptive statistics correctly; know skew/outliers.
• Now: Practice interpretation with percentiles and targets.
• Next: Visual interpretation (box plots, histograms) and comparing groups; then basics of inference (confidence and sampling) to speak about uncertainty.

Mini challenge

Session durations (minutes): [1, 1, 2, 2, 3, 3, 4, 5, 8, 12, 15, 20]

• Write a one-sentence product update using the template: “Typical session is X; 90% of sessions are under Y; distribution is [shape]. Action: [what next].”

Sample answer

“Typical session is ~3 minutes (median); 90% are under 15 minutes; right-skewed with a long tail. Action: Improve onboarding to lift the median.”

Next steps

• Apply the checklist on your next weekly KPI readout.
• Add percentiles to at least one dashboard card that currently shows only an average.
• Practice saying your one-sentence interpretation out loud; refine until it’s clear and specific.

Progress saving note

The quick test below is available to everyone; if you log in, your progress will be saved automatically.

Quick Test

Answer the questions to check your practical interpretation skills.