Cumulative frequency and box plots · Higher · Frequência acumulada e diagramas de caixa · Avançado
| English | Português |
|---|---|
| interquartile range/ˌɪntəˈkwɔːtaɪl reɪndʒ/ | amplitude interquartil |
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? · Qual descrição define corretamente a amplitude interquartil?
The difference between the upper and lower quartiles. · A diferença entre o primeiro e o terceiro quartis.
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 · Frequência acumulada e diagramas de caixa
A cumulative frequency counts observations below successive class boundaries · Uma frequência acumulada conta observações abaixo de limites de classe sucessivos
Compare the model with the worked case and explain one change. · Compare o modelo com o caso resolvido e explique uma mudança.
Find the IQR when Q1=12,Q3=21. · Encontre a amplitude interquartil quando Q1=12,Q3=21.
IQR=Q3-Q1=21-12=9. · AIQ=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. · Para 80 observações, encontre a frequência acumulada usada para a mediana.
The median position is half the total cumulative frequency: 80/2=40. · A posição da mediana é metade da frequência acumulada total: 80/2=40.
The interquartile range always equals the maximum minus the minimum. · A amplitude interquartil sempre é igual ao máximo menos o mínimo.
Plot against class boundaries rather than midpoints. Grouped quartiles are estimates. The range is sensitive to extremes; the IQR describes only the middle half. · Plotar contra limites de classe em vez de pontos médios. Quartis agrupados são estimativas. A amplitude é sensível a extremos; o IQR descreve apenas a metade central.
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. · Para Q1=12, IQR=9, encontre Q1-1.5IQR.
The lower outlier fence is 12-1.5×9=-1.5. · O limite inferior de valores atípicos é 12-1.5×9=-1.5.
Match each part of a complete solution to its purpose. · Associe cada parte de uma solução completa ao seu propósito.
An assumption justifies the model; a check tests the result; interpretation connects it to the question. · Uma suposição justifica o modelo; uma verificação testa o resultado; a interpretação conecta-o à pergunta.
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.