Choosing displays, pie charts and time series · Higher
| English | 中文 | Pinyin |
|---|---|---|
| time series/taɪm ˈsɪəriːz/ | 时间序列 | shí jiān xù liè |
A bar chart compares travel categories, while a line graph shows attendance changing through the week. Joining unrelated categories with a line suggests a false progression.
- A bar chart compares travel categories, while a line graph shows attendance changing through the week. Joining unrelated categories with a line suggests a false progression.
- This lesson studies time series 时间序列: Measurements recorded in time order.
Choose the mathematical structure
- Use separate bars for categories, vertical line charts for discrete numerical values and time-ordered lines for a time series. Pie-chart sector angle is frequency/total×360°. A pictogram needs a stated key and honest fractional symbols. Label axes/units and choose a scale that does not conceal the relevant variation. Continuous grouped distributions need histograms rather than categorical bars.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Which description correctly defines time series?
Measurements recorded in time order.
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.
Of 40 students, 10 walk, 15 take the bus and 15 cycle. Pie angles are 90°,135°,135°, summing to 360°. With one pictogram symbol representing five students, the groups use 2,3,3 symbols. If one symbol instead means four students, ten walkers need 2.5 symbols. A daily attendance time series 32,35,33,36,34 can be joined in weekday order; the largest count is 36 and its range is 4. A frequency table for number of siblings 0,1,2,3 uses those numbers as positions on a vertical line chart, rather than treating widths as probabilities.
Choosing displays, pie charts and time series
Use separate bars for categories, vertical line charts for discrete numerical values and time-ordered lines for a time series
Classify the worked-case statements, then explain the units or invariant that justifies each decision.
Find pie angle for 10 of 40 students.
10/40×360=90°.
Test a tempting shortcut
- A pie chart must represent a complete total with non-overlapping categories. Pictogram keys control the count, not decorative icon size. A truncated axis may exaggerate a small difference; read the scale before comparing.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
A line graph is always the best display for unrelated categories. This claim is false. Explain which definition or assumption it violates.
Find pie angle for 15 of 40.
15/40×360=135°.
A line graph is always the best display for unrelated categories.
A pie chart must represent a complete total with non-overlapping categories. Pictogram keys control the count, not decorative icon size. A truncated axis may exaggerate a small difference; read the scale before comparing.
Interpret a new situation
- AQA S2 covers tables, categorical bars/pies/pictograms, discrete vertical lines and time-series tables/graphs. Explain why the representation fits the variable and the question.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Find pictogram symbols for 10 students if each represents 4.
10/4=2.5 symbols.
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
- 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.
Measurements recorded in time order. Choose the relationship, show the method, check its assumptions and interpret the result.