Cumulative frequency and box plots · Higher · Fréquence cumulée et diagrammes en boîte · Supérieur
| English | Français |
|---|---|
| interquartile range/ˌɪntəˈkwɔːtaɪl reɪndʒ/ | écart interquartile |
Which route is more consistent?
- Two bus routes have similar typical times but different reliability. Quartiles show the middle half of the journeys.
- This lesson studies interquartile range 四分位距: The difference between the upper and lower quartiles.
Choose the mathematical structure
- A cumulative frequency counts observations below successive class boundaries. Read quartiles at one quarter, one half and three quarters of the total frequency. A box plot represents minimum, lower quartile, median, upper quartile and maximum.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Which description correctly defines interquartile range? · Quelle description définit correctement l'écart interquartyle ?
The difference between the upper and lower quartiles. · La différence entre le premier et le troisième quartile.
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.
For 80 observations, read Q1 at cumulative frequency 20, median at 40 and Q3 at 60. If Q1=12,Q3=21, then IQR=9. Compare the medians for typical journey time and the IQRs for consistency.
Cumulative frequency and box plots · Fréquence cumulée et diagrammes en boîte
A cumulative frequency counts observations below successive class boundaries · Une fréquence cumulée compte les observations situées sous les limites de classe successives
Compare the model with the worked case and explain one change. · Compare le modèle avec l'exemple résolu et explique un changement.
Find the IQR when Q1=12,Q3=21. · Trouver l'écart interquartile lorsque Q1=12, Q3=21.
IQR=Q3-Q1=21-12=9. · EIQ = Q3 - Q1 = ⟨21⟩ - ⟨12⟩ = ⟨9⟩.
Test a tempting shortcut
- Plot against class boundaries rather than midpoints. Grouped quartiles are estimates. The range is sensitive to extremes; the IQR describes only the middle half.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
The interquartile range always equals the maximum minus the minimum. This claim is false. Explain which definition or assumption it violates.
For 80 observations, find the cumulative frequency used for the median. · Pour 80 observations, trouver la fréquence cumulée utilisée pour la médiane.
The median position is half the total cumulative frequency: 80/2=40. · La position de la médiane est la moitié de la fréquence cumulée totale : ⟨80⟩ / ⟨2⟩ = ⟨40⟩.
The interquartile range always equals the maximum minus the minimum. · L'écart interquartile correspond toujours au maximum moins le minimum.
Plot against class boundaries rather than midpoints. Grouped quartiles are estimates. The range is sensitive to extremes; the IQR describes only the middle half. · Tracer contre les limites de classe plutôt que les milieux. Les quartiles groupés sont des estimations. L'étendue est sensible aux extrêmes ; l'EIQ décrit uniquement la moitié centrale.
Interpret a new situation
- Explain a comparison in the context of the measured quantity. An outlier rule may use Q1-1.5IQR and Q3+1.5IQR; use the rule specified in the task rather than assuming every graph follows it.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
For Q1=12,IQR=9, find Q1-1.5IQR. · Pour Q1=12, EIQ=9, trouver Q1 - ⟨1.5⟩×EIQ.
The lower outlier fence is 12-1.5×9=-1.5. · La limite inférieure des valeurs aberrantes est ⟨12⟩ - ⟨1.5⟩ × ⟨9⟩ = -1.5.
Match each part of a complete solution to its purpose. · Associer chaque partie d'une solution complète à son but.
An assumption justifies the model; a check tests the result; interpretation connects it to the question. · Une hypothèse justifie le modèle ; une vérification teste le résultat ; l'interprétation le relie à la question.
Use this in your course
- 4MA1 · Higher · 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 difference between the upper and lower quartiles. Choose the relationship, show the method, check its assumptions and interpret the result.