FREE STATISTICS FOR BUSINESS DECISIONS LEARNING PATH

WikiFree original practice workbook

The uncertainty studio

CASE STATUS: fictional/synthetic teaching material. Do not present the example as real research, employment experience or measured business performance.

OUTCOME
Summarize a small business sample, investigate an outlier and write a decision memo that separates observations from unsupported generalizations.

BEFORE YOU START
Basic arithmetic and a spreadsheet or calculator. No calculus or paid statistics package.

CASE
A fictional help desk records six resolved-ticket waiting times on one conveniently chosen afternoon. This is not a random sample of all customers. Units are minutes.

INPUTS
Ticket,Wait minutes
T1,2
T2,3
T3,3
T4,4
T5,6
T6,18


ENTRY CHECK

Question: Is the mean always a typical experience?

Self-check: No. A skewed distribution can pull it away from most cases.

Question: Can correlation prove a cause?

Self-check: No.

Question: Does a large convenience sample remove selection bias?

Self-check: Not automatically.

STAGE 1: Define the population and sample

Prerequisite: Basic arithmetic and a spreadsheet or calculator. No calculus or paid statistics package.

Instruction: Before calculation, define who could have been observed and who actually was. A sample of resolved afternoon tickets excludes unresolved work and other times of day. That selection can bias a service conclusion. Record the sampling method, time window and exclusions. More precise arithmetic cannot repair a poorly matched sample; the first deliverable is a scope statement.

Practice task: Write the target population, observed sample and three likely omissions. Propose a better collection schedule.

Deliverable: A sampling note.

Acceptance check: It names unresolved tickets and other time periods as missing from this sample.

If stuck: Replace claims about all customers with claims about the six observed tickets.

Record your work, decisions and evidence:




Record your result against the acceptance check:



STAGE 2: Describe center and spread

Prerequisite: Bring your previous output: A sampling note.

Instruction: Sort the values before calculating the median. With an even count, average the two middle values. Report units and sample size next to a statistic. Mean, median and range answer different questions; showing several summaries makes the influence of unusual observations visible. Preserve the raw rows so someone else can reproduce your summary.

Practice task: Calculate mean, median, minimum, maximum and range. Draw a dot plot with one mark per ticket.

Deliverable: A labeled descriptive table and dot plot.

Acceptance check: Mean 6; median 3.5; minimum 2; maximum 18; range 16 minutes; n=6.

If stuck: Do not average only unique values or leave units off the chart.

Record your work, decisions and evidence:




Record your result against the acceptance check:



STAGE 3: Investigate the long wait

Prerequisite: Bring your previous output: A labeled descriptive table and dot plot.

Instruction: An unusual value is a question, not permission to delete a row. Check whether 18 is an entry error, a valid exception or evidence of a different process. Compare the full sample with a clearly labeled sensitivity summary that excludes it. The five-row mean becomes 3.6, showing why the exclusion decision materially changes the story.

Practice task: Create an issue log for T6 and compute summaries with and without it. Keep both versions and state which is primary.

Deliverable: An outlier investigation and sensitivity comparison.

Acceptance check: The six-row summary remains primary unless evidence supports correction; the exclusion is disclosed.

If stuck: Never silently remove a slow ticket because it makes service look better.

Record your work, decisions and evidence:




Record your result against the acceptance check:



STAGE 4: Separate relationship from explanation

Prerequisite: Bring your previous output: An outlier investigation and sensitivity comparison.

Instruction: A relationship between two measured variables may arise from other factors or the collection process. Our six rows contain only waiting time; they cannot establish whether staffing caused the long wait. A sound next study records relevant context, defines comparable groups and checks alternative explanations. Do not draw a causal chart from columns that were never collected.

Practice task: Draft a follow-up data dictionary containing shift, arrival time, queue size and staffing count. Write a testable association question and two alternative explanations.

Deliverable: A follow-up study plan.

Acceptance check: The plan distinguishes an association question from a causal claim and defines each field.

If stuck: If the memo says understaffing caused T6, replace that statement with an evidence request.

Record your work, decisions and evidence:




Record your result against the acceptance check:



STAGE 5: Write a proportion carefully

Prerequisite: Bring your previous output: A follow-up study plan.

Instruction: An observed proportion is a count divided by a defined denominator. Here five of six tickets waited at most six minutes. That fraction is descriptive; it is not a reliable promise about the next customer or a population confidence statement. A decision memo should show the fraction, the small sample and the collection limits together.

Practice task: Calculate the observed share at or below six minutes. Write a 200-word memo recommending one next collection action.

Deliverable: A bounded statistical decision memo.

Acceptance check: It states 5/6, about 83.3%, for this sample only and avoids an unsupported population guarantee.

If stuck: Do not convert the sample proportion into a service-level promise.

Record your work, decisions and evidence:




Record your result against the acceptance check:



WORKED CASE
The sample mean is 6 minutes, while the median is 3.5. Excluding T6 changes the mean to 3.6; that is a sensitivity result, not a cleaned truth. The next useful action is broader, consistently collected evidence rather than an immediate causal verdict.

FINAL PROJECT
Deliver the raw table, summaries, dot plot, outlier log and decision memo. Add waits of 5 and 7 from the next shift, recalculate all summaries and explain why the expanded convenience sample still has limits.

REQUIRED CRITICAL CHECK
No row is silently removed and no sample result is presented as proven causation or a population guarantee.

SCORING
Score each of the five stage acceptance checks from 0–16 (0 missing/incorrect; 8 partially supported; 16 complete and evidenced). Score the final integrated project from 0–20 (0 missing; 10 incomplete handover; 20 complete, reproducible and consistent with the case). Target: at least 80/100 AND the critical check must pass. A total score never overrides a failed critical check.

SCOPE LIMIT
This is descriptive statistical reasoning, not a complete inference, forecasting or experimental-design course.

SOURCES AND ACCESS
Assigned public videos can be watched free. Complete the original case in a text editor, on paper or in a spreadsheet you already have. No paid course, exam or provider certificate is included.

Statistics for Finance: Free Course
WikiFree: https://wikifree.com/courses/free-aswath-damodaran-statistics-for-finance/
Official source: https://www.youtube.com/playlist?list=PLUkh9m2BorqmXcRzWFbzcjMd7fYErVexF
Why selected: Selected public statistics lessons cover sampling, description, distributions, relationships and probability; finance applications are not assigned.

Stage 1 selected lessons:

2. Session 1: Introduction to statistics (16:50)
https://www.youtube.com/watch?v=w0dsBZn7DsI&list=PLUkh9m2BorqmXcRzWFbzcjMd7fYErVexF&index=2

3. Session 2: Sampling in Statistics (24:14)
https://www.youtube.com/watch?v=zVAgoo9mg74&list=PLUkh9m2BorqmXcRzWFbzcjMd7fYErVexF&index=3

Stage 2 selected lessons:

5. Session 3: Descriptive Statistics (19:26)
https://www.youtube.com/watch?v=uKstNleBOkA&list=PLUkh9m2BorqmXcRzWFbzcjMd7fYErVexF&index=5

Stage 3 selected lessons:

7. Session 4: Statistical Distributions (14:56)
https://www.youtube.com/watch?v=mWjkdCZ0URE&list=PLUkh9m2BorqmXcRzWFbzcjMd7fYErVexF&index=7

Stage 4 selected lessons:

9. Session 5: Data Relationships (31:59)
https://www.youtube.com/watch?v=5HIVw3kvZ20&list=PLUkh9m2BorqmXcRzWFbzcjMd7fYErVexF&index=9

Stage 5 selected lessons:

12. Session 6: Probability and Probabilistic Tools (24:54)
https://www.youtube.com/watch?v=u-NuNKCkmR0&list=PLUkh9m2BorqmXcRzWFbzcjMd7fYErVexF&index=12

REUSE
Original WikiFree teaching text and synthetic fixtures are supplied for personal learning and adaptation with attribution. Provider lessons remain on their original sites and retain their own terms. No provider certificate is included.