MathematicsChapter 11: Basic Statistics
Boundaries That Close Gaps
Subtract 0.5 from each lower limit and add 0.5 to each upper limit when classes are whole numbers that skip (1-10 then 11-20).
Learning objectives
- Define and explain boundaries that close gaps.
- Apply boundaries that close gaps to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
Subtract 0.5 from each lower limit and add 0.5 to each upper limit when classes are whole numbers that skip (1-10 then 11-20). That 0.5 step is how you close gaps. The shared wall is 10.5. Histograms use these walls as the bases of rectangles so there is no empty strip between 10 and 11. If classes are already continuous (0-10, 10-20 with 10 sitting on a stated rule), the given ends may already be
Where / symbols
- Boundaries That Close Gaps
- Subtract 0.5 from each lower limit and add 0.5 to each upper limit when classes are whole numbers that skip (1-10 then 11-20). That 0.5 step is how you close gaps. The shared wall is 10.5. Histograms use these walls as the bases of rectangles so there is no empty strip between 10 and 11. If classes are already continuous (0-10, 10-20 with 10 sitting on a stated rule), the given ends may already be
Overview
Learn the idea, then use it:
Core Understanding
Subtract 0.5 from each lower limit and add 0.5 to each upper limit when classes are whole numbers that skip (1-10 then 11-20). That 0.5 step is how you close gaps. The shared wall is 10.5. Histograms use these walls as the bases of rectangles so there is no empty strip between 10 and 11. If classes are already continuous (0-10, 10-20 with 10 sitting on a stated rule), the given ends may already be
Examples close gaps · 0.5 · lower · BOUNDARIES THAT CLOSE GAPS: Subtract 0.5 from each lower limit and add 0.5 to each upper limit when classes are whole numbers that skip (1-10 then 1
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — BOUNDARIES THAT CLOSE GAPS
Subtract 0.5 from each lower limit and add 0.5 to each upper limit when classes are whole numbers that skip (1-10 then 11-20). That 0.5 step is how you close gaps. The shared wall is 10.5. Histograms use these walls as the bases of rectangles so there is no empty strip between 10 and 11. If classes are already continuous (0-10, 10-20 with 10 sitting on a stated rule), the given ends may already be
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge boundaries that close gaps with a neighbouring idea that uses a different definition, rule, or method.
Key points
- close gaps
- 0.5
- lower
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Boundaries That Close Gaps
Sticky Notes · Quick Revision
Core Idea
- Subtract 0.5 from each lower limit and add 0.5 to each upper limit when classes are whole numbers that skip (1-10 then 11-20).
Key Points
- close gaps
- 0.5
- lower
Simple Check
- Explain boundaries that close gaps in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge boundaries that close gaps with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- Subtract 0.5 from each lower limit and add 0.5 to each upper limit when classes are whole numbers that skip (1-10 then 11-20).
- close gaps
- 0.5
- lower
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