Compare averages with the underlying distribution
See this course’s project requirements
Audit the supplied fictional claim about a reminder app using sampling, summary, conditional-rate, uncertainty, and causal-reasoning tools.
Keep your working files in your own notebook or software. Save a private description, checklist, and work link in My Proof.
What to include
- Identify the claim, population, sample, unit of observation, and sampling limits.
- Calculate and compare mean, median, absolute change, and relative change where appropriate.
- Use a natural-frequency table to compute a conditional percentage with the correct denominator.
- Interpret a supplied confidence interval without treating it as individual variation or certainty.
- Write a claim verdict that separates supported description from unsupported causation and names needed evidence.
Review and revise
Use these criteria to check your work and choose what to improve.
- Calculation: quantities and denominators are correct and reproducible.
- Scope: sample and population claims are distinguished.
- Uncertainty: intervals and study limits are explained accurately.
- Judgment: the conclusion is proportional to the evidence and identifies a useful next question.
Want more background?
The idea in everyday life
An average can be numerically correct while giving a misleading impression of a typical experience. Mean and median answer different summary questions, especially when values are uneven. You will use a small fictional waiting-time dataset that can be checked by hand. The goal is to choose informative wording, not declare one summary universally superior to another.
A summary compresses data; inspect what that compression hides.
One step at a time.
Use the sample or information you have permission to use. Keep your work as you go. You can pause between steps.
- 1
Copy and sort the five fictional wait times. Count the observations before calculating any summary, and retain minutes as the unit throughout the worksheet.
- 2
Calculate the mean by summing all five values and dividing by five. Find the median by locating the middle value in the ordered list.
- 3
Calculate the minimum, maximum, and range. Describe how the single thirty-minute wait influences the mean compared with the median without deleting it merely because it is unusual.
- 4
Replace the last value with ten in a clearly labeled hypothetical variant and recompute both summaries. Compare the changes to see which measure responds more strongly here.
- 5
Write a two-sentence description that includes a useful center and the spread or unusual value. Save both calculations and explain which question each summary helps answer.
See how it works.
Fictional scenario: Five waiting times are 4, 5, 5, 6, and 30 minutes. Their sum is 50, so the mean is ten minutes; the middle ordered value, five, is the median. Four people waited six minutes or less, while one waited thirty. Casey rejects the statement “everyone waits ten minutes” because the mean is not an individual value for every person. Casey reports both summaries and the long wait. If the purpose is total staffing demand, the mean may be useful; if describing the middle experience, the median adds a different perspective.
Did you cover these?
- Original mean is ten minutes and median is five.
- Original range is 26 minutes.
- The ten-minute variant has mean six and median five.
What to finish
A mean/median comparison with range, a hypothetical variant, and an accurate description of the waits.
Watch for this
Calling a mean the experience of every person or discarding a legitimate extreme value without explanation.
How can I tell I understand it?
You calculate both centers and choose wording that acknowledges the distribution.
Quick knowledge check
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Source & access notes · checked 2026-09-10
Opened the section on mean and median. All wait-time datasets in this course are original.
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Reuse: Linked for further study. Life Starter explanations, scenarios, and assessments are original; free access alone does not grant reuse rights.
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