Centre, spread and data displays · Core
| English | 中文 | Pinyin |
|---|---|---|
| range/reɪndʒ/ | 极差 | jí chà |
Can one average tell the whole story?
- Two groups have the same median but different spread. One summary cannot describe both location and consistency.
- This lesson studies range 极差: The maximum observed value minus the minimum observed value.
Choose the mathematical structure
- The mean is total divided by count. The median is the central value after sorting. The range is maximum minus minimum. Use frequency tables, bar charts and suitable comparisons.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Which description correctly defines range?
The maximum observed value minus the minimum observed value.
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 2,4,4,6,9, total=25 and count=5, so mean=5. The central value is 4, so median=4. The range is 9-2=7. Explain both a typical value and the spread.
Centre, spread and data displays
The mean is total divided by count
Choose a centre and a spread measure for the worked observations.
Find the range of 2,4,4,6,9.
Range=maximum-minimum=9-2=7.
Test a tempting shortcut
- The tallest histogram bar need not contain the most observations. A grouped mean is an estimate. Correlation does not prove causation, and extrapolation extends beyond the observed range.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
The mean of a list must always be one of its observed values. This claim is false. Explain which definition or assumption it violates.
Find the mean of 2,4,4,6,9.
The total is 25 across five observations: mean=25/5=5.
The mean of a list must always be one of its observed values.
The tallest histogram bar need not contain the most observations. A grouped mean is an estimate. Correlation does not prove causation, and extrapolation extends beyond the observed range.
Interpret a new situation
- A bar chart uses separate bars for categories. Unequal-class-width histograms and formal density calculations are outside this Foundation/Core lesson.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Find the median of 2,4,4,6,9.
The sorted list is 2,4,4,6,9. Its third observation is 4.
Match each part of a complete solution to its purpose.
An assumption justifies the model; a check tests the result; interpretation connects it to the question.
Use this in your course
- 9260 · Core · 3.4. 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 maximum observed value minus the minimum observed value. Choose the relationship, show the method, check its assumptions and interpret the result.