Free statistics classroom activity
Students run two strategies repeatedly, summarize center and spread, investigate unusual results, and decide whether the evidence supports a cautious recommendation. No account or personal information is required.
Business Statistics & Distribution Lab
Compare two operating strategies across repeated simulation trials, compute automated sample mean ($\mu$), median, and range, inspect distribution overlap, and balance primary gains against operational guardrails.
Direct answer
Treat each completed run as one observation, not as proof. Students hold the scenario and most decisions steady, repeat a baseline strategy, repeat one alternative, and record the same outcome each time. The two small distributions reveal whether a difference is large compared with variation inside each strategy.
Mean describes arithmetic center, median identifies the middle ordered result, and range gives a quick view of spread. When these summaries disagree or the distributions overlap, students inspect individual values before making a claim instead of selecting whichever strategy had the single best run.
Standardized statistical samples
To ensure repeated simulation trials generate fair, comparable sample distributions without hidden parameter drift, initialize Strategy A and Strategy B runs using 1-click classroom scenario launch codes. Controlled baseline conditions across all 18 business simulators allow students to compute valid means, medians, ranges, and distribution overlaps.
Investigation menu
| Simulation | Compare | Primary statistic | Guardrail | Worksheet |
|---|---|---|---|---|
| Lemonade stand | Two prices or batch sizes | Profit or cups sold | Waste or unmet demand | Open |
| Restaurant | Two staffing levels | Customers served | Rating or labor cost | Open |
| Coffee shop | Two price-quality plans | Transactions or profit | Queue or waste | Open |
| Bakery | Two production quantities | Units sold or profit | Stockouts or waste | Open |
| Fitness studio | Two membership plans | Members or profit | Churn or utilization | Open |
| Car wash | Two package or labor plans | Cars served or profit | Wait or quality | Open |
Use one primary outcome for the statistical comparison and one guardrail to catch a harmful tradeoff. Keep units and reporting periods consistent.
Ready-to-use sequence
Learning goal: compare two small distributions using center, spread, individual values, and a qualified business interpretation.
Printable student record
Business and scenario: ______________________________________________
Question: How does changing __________________ affect __________________?
Prediction and reason: ______________________________________________
Strategy A: __________________ Strategy B: __________________
Held constant: ______________________________________________________
Primary outcome and unit: __________________ Guardrail and unit: __________________
| Measure | A1 | A2 | A3 | B1 | B2 | B3 |
|---|---|---|---|---|---|---|
| Primary outcome | ||||||
| Guardrail outcome | ||||||
| Unexpected condition |
| Summary | Strategy A | Strategy B | Interpretation |
|---|---|---|---|
| Ordered values | Show values first. | ||
| Mean | B − A = ______ | ||
| Median | B − A = ______ | ||
| Range | Which varied more? | ||
| Possible outlier | Keep, investigate, or exclude—with reason. | ||
| Guardrail | Did the gain create a tradeoff? |
Mean: sum the values and divide by the number of trials.
Median: order values and select the middle; with an even count, average the two middle values.
Range: maximum − minimum. It gives a quick view of spread but not every distribution feature.
Percentage-point difference: subtract one rate from another. From 72% to 78% is 6 percentage points.
Relative percent change: (new − original) ÷ |original| × 100%. State the baseline and avoid it when the baseline is zero.
Never remove a result only because it weakens a preferred claim. Record the rule and reason, then report whether the conclusion depends on it.
Sentence frame: Across ___ trials, strategy ___ had a mean ___ of ___ versus ___, while medians were ___ and ___. The ranges ___, suggesting ___. We recommend ___ inside this model, but would collect ___ before a real decision.
| Criterion | 3 — strong | 2 — developing | 1 — beginning | 0 — missing |
|---|---|---|---|---|
| Comparable data | Clear strategies, repeated trials, constant conditions, complete units. | Mostly comparable with a minor gap. | Few trials or inconsistent units. | No usable comparison. |
| Calculations | Mean, median, range, and differences are accurate and shown. | One minor error. | Several errors or missing work. | No summaries. |
| Distribution reasoning | Uses values, center, spread, outlier, overlap, and tradeoff. | Interprets center and some variation. | Relies on one average or best run. | No interpretation. |
| Recommendation | Evidence-based, qualified, model-bounded, with a next test. | Plausible with partial qualification. | Overclaims or weak evidence link. | No supported decision. |
Grade reasoning and transparent uncertainty, not the largest profit. The full assessment rubric adds feedback codes and group-work guidance.
Require units and sensible rounding. Three trials with a mean of $143.333 do not justify a tenth of a cent. Ask what precision the inputs and decision support.
Provide two approved strategies, a six-value dataset, and a calculation organizer. Let students explain center and spread verbally before writing.
Collect five trials, graph dot plots, calculate interquartile range, compare class groups, or predefine an outlier rule. More simulated trials reduce some uncertainty without making the model representative.
These observations come from simplified educational rules, not sampled customers, employees, competitors, or markets. More runs can describe the model more precisely but cannot correct missing variables or establish real-world validity.
Do not collect student personal information or invent survey responses. Real research needs permission, privacy protection, truthful methods, current legal and safety requirements, reliable source data, and stakeholder input. Simulator results are not financial, legal, operational, or market advice.
Lemonade Stand, Restaurant, Coffee Shop, and Bakery offer accessible measures. Any simulator works with comparable repeated conditions.
Mean, median, range, differences, and possible outliers, followed by a distribution-based interpretation.
Three per strategy fit this lesson. Five or more show variation better, but remain a small model-generated sample.
No account, name, email, download, or personal information is required.
No. They describe a simplified model, not a representative real-world sample.
Use the business math lesson for break-even and margin, the data analysis lesson for controlled comparisons, the results-analysis guide to interpret absolute, relative, and percentage-point changes, the charts and data visualization guide to display comparisons, trends, distributions, and relationships honestly, the benchmarking guide to compare matched runs with medians, quartiles, normalization, and guardrails, the business analytics lesson to organize outcomes, drivers, and guardrails into a decision dashboard, the business calculators to check formulas, or the teacher hub for more activities.