Explain a hard idea simply
Create an accurate explanation for a specified reader.
Complete prompt
Task
Create an accurate explanation for a specified reader.
Instructions
Explain [IDEA] to [AUDIENCE] who already knows [PRIOR KNOWLEDGE]. Start with a one-sentence answer, then use one concrete example and one boundary case. Define necessary terms. Mark uncertainty and avoid a claim stronger than the evidence.
Expected output
Answer, example, boundary case, and a short “what this does not mean” section.
Checks
- The audience is respected.
- Every technical term is defined.
- Limits are explicit.Expected output and checks
Expected output
Answer, example, boundary case, and a short “what this does not mean” section.
Checks
- The audience is respected.
- Every technical term is defined.
- Limits are explicit.
Worked example
Explain a hard idea simply: recorded example
Original input
Task
Create an accurate explanation for a specified reader.
Instructions
Explain weighted averages: groupA has10 people with mean score4, groupB has30 people with mean score8. All numbers are fictional. to adult community volunteers who already knows ordinary arithmetic mean but not weighted mean. Start with a one-sentence answer, then use one concrete example and one boundary case. Define necessary terms. Mark uncertainty and avoid a claim stronger than the evidence.
Expected output
Answer, example, boundary case, and a short “what this does not mean” section.
Checks
- The audience is respected.
- Every technical term is defined.
- Limits are explicit.
What the checks found
- Independent calculation gives (10×4 + 30×8) / 40 = 7. The equal-group boundary example correctly gives 6.
- The explanation defines the weight and distinguishes a mean from individual scores and spread.
Revisions after the first output
- No correction needed for the supplied numbers.
Original output
The combined mean score is 7, because the group of 30 people contributes three times as much to the overall average as the group of 10.
Example
A weighted mean is an average in which each value contributes according to its weight, meaning how much it counts. When combining group means, the weight is the number of people in each group, so each person counts equally.
Imagine combining the fictional scores of two groups of community volunteers:
- Group A: 10 people with mean score 4 → total score 10 × 4 = 40.
- Group B: 30 people with mean score 8 → total score 30 × 8 = 240.
- Together: 40 people and total score 280 → combined mean 280 ÷ 40 = 7.
Simply averaging the two group means, (4 + 8) ÷ 2 = 6, would give the smaller group the same influence as the larger group. Counting all 40 people equally gives 7 instead.
Boundary case
If both groups had 10 people, their weights would be equal. Then the combined mean would be (10 × 4 + 10 × 8) ÷ 20 = 6, the same as the ordinary average of the two group means.
What this does not mean
A mean of 7 does not mean everyone scored 7, or even that anyone scored exactly 7. It does not tell us how spread out the scores are or why the groups differ. The result is exact if the supplied means are exact, the groups do not overlap, and scores use the same scale. If the means were rounded, 7 would be an approximate combined mean. These fictional numbers establish no claim about real volunteers.