Quartiles, box plots and distribution comparisons · Higher
導入済み| English | 意味 |
|---|---|
| interquartile range/ˌɪntəˈkwɔːtaɪl reɪndʒ/ | 四分位距 |
Two classes can have the same median but different consistency. A box plot shows the middle half separately from the extreme observations.
- Two classes can have the same median but different consistency. A box plot shows the middle half separately from the extreme observations.
- This lesson studies interquartile range 四分位距: The upper quartile minus the lower quartile.
Choose the mathematical structure
- A box plot marks minimum, lower quartile Q1, median, upper quartile Q3 and maximum, or identifies separately shown outliers according to the stated convention. IQR=Q3-Q1 describes the middle half. Compare median and IQR in context; a smaller IQR suggests less middle-half variation, not necessarily a smaller full range. Quartile conventions vary for a finite raw list, so follow the task or supplied summaries.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Groups A and B both have median 8, but A has IQR 6 and B has IQR 4. What does the comparison support?
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
The IQR measures the middle 50% only: B’s smaller IQR means its central values cluster tighter. The full range includes extremes, which B has - a wider whisker does not undo the tighter box.
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
Group A has summary 2,5,8,11,18 and group B has 1,6,8,10,20. Both medians are 8. A has IQR=6 and range=16; B has IQR=4 and range=19. B’s middle half is more consistent although its full range is larger. Under a stated 1.5×IQR outlier rule, A’s fences are 5-9=-4 and 11+9=20; a new value 23 lies above the upper fence. This rule is a specified convention, not a compulsory rule for every box plot. When using cumulative frequency, read Q1 at N/4 and Q3 at 3N/4, then subtract; small reading errors affect the estimated IQR.
Quartiles, box plots and distribution comparisons
A box plot marks minimum, lower quartile Q1, median, upper quartile Q3 and maximum, or identifies separately shown outliers according to the stated convention
Classify the worked-case statements, then explain the units or invariant that justifies each decision.
Find IQR for Q1=5,Q3=11.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
11-5=6.
Test a tempting shortcut
- The median line need not be halfway along the box. Equal medians do not mean identical distributions. Whisker meanings depend on whether outliers are drawn separately; read the stated convention.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
Equal medians prove that two groups have the same spread. This claim is false. Explain which definition or assumption it violates.
Find range for minimum 2,maximum 18.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
18-2=16.
Equal medians prove that two groups have the same spread.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
The median line need not be halfway along the box. Equal medians do not mean identical distributions. Whisker meanings depend on whether outliers are drawn separately; read the stated convention.
Interpret a new situation
- AQA S4 Higher adds box plots, quartiles and IQR to distribution comparisons. Name both centre and spread, with units and context, and avoid claims about all observations from just the box.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Under the stated 1.5 IQR rule, find the upper fence for those quartiles.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
11+1.5×6=20.
Match each box-plot feature to its meaning.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
Compare median for the typical value and IQR for consistency, and read the stated convention before interpreting whiskers or outliers.
Use this in your course
- 8300 · Higher · 3.6. Match the target tier and specification before assigning extensions.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
The upper quartile minus the lower quartile. Choose the relationship, show the method, check its assumptions and interpret the result.