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A single case is the right evidence for some claims and no evidence at all for a claim about how often.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
You will take a vivid single case, say exactly what it is evidence for, and work out how many cases it is silent about. You will then decide, for a claim on the table, whether one case settles it or whether only a count can — and mark the step that puts one story against a figure.
You can ask what a claim is resting on. Here the thing it rests on is a story, and the question is the same as everywhere else in this course: what does this reach, and where does it stop?
| Term | What it means |
|---|---|
| Anecdote | A report of a particular case whose accuracy and scope still need checking. |
| Numerator | The relevant events or affected cases counted above the fraction bar. |
| Denominator | The matching group or exposure against which the count is compared. |
| Mean | The sum of measured values divided by the number of values. |
| Selection | The process determining which cases enter a report or collection. |
Jonas had his bike taken from the rack in March. Suppose it is completely true. What have you learned?
You have learned that the rack had at least one theft that month. That is a real fact and it is evidence — evidence that it can happen there, which is not nothing at all.
What you have not learned is how often. The club has two hundred and forty members; the story is about one of them; and the other two hundred and thirty-nine are still uncounted. Somebody who hears the story and stops locking their bike, or starts, has taken one observation for a rate.
The arithmetic makes this hard to forget. Write down the number the story is one of, and the number it is silent about. The second number is nearly always enormous, and seeing it written is more convincing than any warning about anecdotes.
Another way: picture
Draw a row of two hundred dots and color one of them in. The colored dot is the story. Everything you have been told about is inside that one dot, and the question how often? is a question about the whole row.
Another way: steps
Three steps whenever a story is offered:
Stories are not second-class evidence. They are first-class evidence for some claims and no evidence for others, and the claim decides which.
| The claim | Does one case settle it? |
|---|---|
| It happened to somebody | yes — here is the somebody |
| It can happen here | yes — it just did |
| It never happens | yes — one case contradicts it outright |
| It happens often | no — that is a count |
| Most people find it so | no — that is a count |
A story also does something a count cannot: it says what the thing is actually like. Twenty-six minutes on average and I sat there watching the clock for two hours are both true, and the second tells you what the tail of the distribution feels like from inside. The mistake is only ever swapping one for the other.
A story usually makes one event vivid: a stolen bicycle, a delayed appointment, or a faulty replacement part. A rate needs two linked quantities. The numerator counts the relevant events or affected people. The denominator states the matching group or exposure. Nine thefts among 240 tracked riders is not the same kind of quantity as nine thefts across 240 parking visits, because one rider can make many visits. Write the unit beside each count before dividing.
Suppose a club tracked 240 riders who used one bicycle rack during a year, and nine of those riders reported a theft from that rack during the year. The proportion of tracked riders reporting at least one theft is 9 divided by 240, or 3.75 percent. This is not automatically a theft probability per parking visit. To estimate that different quantity, you would need the relevant count of visits and a clear rule for counting theft events. The correct denominator follows the question being asked.
Now suppose you initially hear only one verified theft story from that group. It establishes at least one affected rider, so it is compatible with many different final totals: one, nine, or more. With the defined group of 240, it even supplies a minimal lower bound of one affected rider in that group. It does not establish the full rate. Saying that a story cannot settle a frequency is more accurate than saying it has literally no evidential value. Its value and its limits can both be stated.
Before comparing two rates, align definitions and time periods. A second rack with three affected riders out of 60 has a 5 percent proportion under the same definitions. Three is fewer than nine, but 3/60 is greater than 9/240. The smaller raw event count does not by itself identify the lower rate. Differences in follow-up, use, reporting, and rider populations would still matter before making a broad judgment about which rack is safer.
Stories often hide the denominator because successes or failures are memorable while uneventful cases disappear. A repair shop may advertise three spectacular successes without saying how many repairs it attempted. A complaint page may collect unhappy customers while satisfied customers have little reason to post. Neither source is automatically dishonest. The selection process determines what the collection can describe. Ask how a case could enter the collection and which cases are likely to remain invisible.
The same person can also tell a story many times. Ten articles about one failed repair are not ten independent failures. Conversely, a single detailed report might document ten separately verified failures. Count the underlying cases rather than headlines, quotations, or emotional intensity. A good evidence summary names the number of distinct observations, how they were selected, and the population or period the proposed conclusion concerns.
An average describes a collection; it does not claim that every member of the collection equals the average. Five waiting times of 10, 20, 25, 30, and 45 minutes sum to 130 minutes, giving a mean of 26. The ten-minute wait is perfectly consistent with that mean. It is one of the observations used to calculate it. Finding that short wait does not expose an arithmetic error unless someone had claimed that every wait was exactly 26 minutes.
The long wait also matters. A person who waited 45 minutes had an experience worse than the mean suggests if it is read carelessly as a promise. The mean can be arithmetically correct while omitting information important to a practical decision. Ask for the spread, the longest waits, or the share exceeding a meaningful threshold. In this five-case collection, one of five waits exceeds 30 minutes. That is 20 percent of this collection, not automatically a forecast for every future day.
A detailed account can identify a mechanism or a question that aggregate figures conceal. A person may describe how an inaccessible entrance prevented them from joining a session even though the overall attendance count was high. The account can establish a particular barrier if verified and can motivate inspecting similar cases. It need not claim that every person experienced that barrier. Quantitative frequency and qualitative detail answer different questions and can improve each other when kept connected to their evidence.
One case can also reveal a data error. If a report claims to include every appointment on Tuesday but a verified appointment record is missing, that case challenges the report's completeness. This differs from merely observing a short wait inside an average. The objection identifies a mismatch between the method claimed and the data actually included. The useful question is which precise claim the story contradicts: the existence of variation, a universal assertion, or the completeness of the dataset.
Verification remains important. An anecdote is a report, not an automatic guarantee that its event occurred exactly as remembered. Ask about records, timing, and alternative explanations in proportion to the claim's importance. If the exercise states that a case is verified, accept that premise for the exercise. Outside a stipulated example, the evidential status of the story is part of the analysis. A dramatic but unverified report should not silently become a confirmed counterexample.
When presenting your conclusion, use wording that fits the evidence. 'One verified rider experienced a theft at this rack' is a supported event claim. 'Nine of 240 tracked riders reported a theft during this year' is a supported summary of a defined collection. 'This rack will always be safe' and 'everyone using it will lose a bicycle' are much stronger claims that neither statement establishes. The discipline is to preserve the scope rather than choosing between celebrating a story and dismissing it.
A fictional advice desk publishes the mean wait for five appointments on a quiet morning. Its complete timing record is 10, 20, 25, 30, and 45 minutes. Adding the waits gives 130 minutes. Dividing by five gives a mean of 26 minutes. A visitor who waited ten minutes says the average must be wrong because their own experience was much faster.
The visitor's record and the desk's arithmetic can both be correct. Ten is one of the five numbers included in the mean. To challenge the mean, the visitor would need to identify a mistaken time, a missing appointment, an incorrect denominator, or an arithmetic error. A difference between one observation and the mean is not enough. The comparison becomes clearer when both the complete list and the individual story are visible.
Another visitor waited 45 minutes and says the mean hides a difficult experience. That criticism can be fair even though the arithmetic is right. One of five visitors waited more than 30 minutes, so the desk could report both the 26-minute mean and the one-in-five share exceeding that threshold for this morning. It should not promise that every future wait will be 26 minutes or less.
The two stories have therefore prompted different questions. The first requires explaining what a mean represents. The second suggests an additional useful measure of variation. Neither requires discarding the count. A good public summary could give the sample size, period, mean, and longer-wait share, while a detailed account helps explain what the delay meant for the person affected. The evidence becomes stronger when those roles are kept distinct.
Answering a figure with a story. My aunt was seen in ten minutes, so the twenty-six-minute average is nonsense is one case put against three thousand, and the average is perfectly happy to contain the aunt.
Throwing every story away. A single case settles it can happen, contradicts it never happens, and is the only thing that tells you what the experience is like.
Forgetting the story is one of the count. Jonas's bike is in the nine. His story is not extra evidence beside the figure; it is a magnified view of one of the nine the figure already counted.
List the five measured waits.
10, 20, 25, 30, 45 minutes.
A complete list makes the individual case and collection comparable.
Add the values.
10 + 20 + 25 + 30 + 45 = 130 minutes.
The mean uses the total of all five waits.
Divide by the count.
130 ÷ 5 = 26 minutes.
Five observations contribute to the reported average.
Locate the anecdote.
The ten-minute wait is the first observation in the list.
An individual value can differ from the mean without contradicting it.
State the supported conclusion.
The visitor's ten-minute story and the 26-minute mean are compatible.
The mean does not assert that every person waited exactly 26 minutes.
Define matching rider groups.
Rack A: 9 of 240; rack B: 3 of 60, over the same period and definition.
Comparable rates require aligned groups and event definitions.
Calculate the first proportion.
9 ÷ 240 = 0.0375 = 3.75%.
The numerator counts affected riders and the denominator tracked riders.
Calculate the second proportion.
3 ÷ 60 = 0.05 = 5%.
The same kind of fraction is used for the second group.
Compare proportions instead of raw counts.
3 is less than 9, but 5% is greater than 3.75%.
Different denominators change the meaning of an event count.
Preserve the comparison's limits.
These are reported yearly rider proportions, not per-visit probabilities.
A different exposure question would need a different denominator.
State the report's methodological claim.
Every Tuesday appointment is included in the dataset.
This is a universal claim about coverage rather than a claim about one typical wait.
Identify a separately verified appointment.
A timestamped Tuesday appointment receipt records a 50-minute wait.
The case has a stated evidential basis beyond memory alone.
Check the published records.
That appointment appears nowhere in the complete exported list.
The missing entry conflicts with the claimed coverage.
Draw the limited criticism.
The dataset's completeness claim is false under these facts.
One omitted qualifying case is enough to refute every appointment included.
Avoid guessing the corrected average.
The missing case must be added before recomputing the mean.
The story reveals a coverage error but does not state every value needed for a new total.
Specify the repair.
Verify all Tuesday records, update the count and sum, then publish the corrected mean.
Repairing the method addresses the actual defect instead of replacing a collection with a single anecdote.
State the verified event.
One phone charged fully in eleven minutes in the recorded test.
The observation establishes what happened under those test conditions.
State the broader claim separately.
All phones of this model always charge in eleven minutes.
The claim extends to many devices and conditions not observed in the one test.
Limit the conclusion.
Four claims about the same set of tablets. For each, say what kind of claim it is, and then what it would take to settle it.
| Who the claim is about | What kind of claim? | What would settle it? | |
|---|---|---|---|
| Somebody who took the tablets came out in a rash | one person | ||
| About one taker in twenty comes out in a rash | all takers | ||
| Nobody who takes the tablets ever comes out in a rash | all takers | ||
| Most people who take the tablets come out in a rash | all takers |
A defined group contains 240 riders. Verified stories describe thefts affecting nine different riders, while no outcomes are supplied for the others. Complete the scope analysis without assuming silence means no theft.
Record the number of described riders.
Known affected cases: known.
The account identifies that many different people rather than nine repetitions of one story.
Find the members not described.
Group size minus known affected cases = unknown riders.
Those members' outcomes have not been supplied.
Calculate the known-case proportion of the defined group.
Known affected cases divided by group size, times 100 = percent percent.
This is a lower bound from the known cases, not a claim that every remaining rider was unaffected.
A club has 235 members. Last year 11 of them had a bike taken from the rack. Jonas tells you his story, and his is one of the 11. How many members had no bike taken?
Answer:
The same club of 187 members, with 3 bikes taken last year. Fill in the two numbers that put the story in its place.
The story is one of a cases, and it says nothing about the other b members.
A complete five-appointment dataset has waits 10, 20, 25, 30, and 45 minutes, with a checked mean of 26. One visitor accurately reports the ten-minute wait. Construct the supported links without confusing an individual value with the average.
This task has no paper form; do it on a device.
A report on a new road layout says that collisions at the junction fell from thirty-one a year to four. Tomas says he was nearly hit there last week. What has Tomas shown?
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
A group has 175 registered riders. Verified accounts describe thefts affecting seven different riders during the year; the other riders' outcomes are not given. Enter the number of known affected riders, the number whose outcomes remain unspecified, and the minimum known affected percentage of the defined group.
Known known; unspecified unknown; minimum percentage percent.
You can say what one case settles and what it leaves untouched, and you can work out how many people a story says nothing about. Explain to somebody why an average of twenty-six minutes and a ten-minute wait are not in disagreement. Next: the claims one case really does settle.
13. One phone and a fleet-wide claim, step 3
The test shows the result can occur, while frequency and consistency need further suitable observations.
A single success does not establish a universal performance guarantee.