Choosing displays, pie charts and time series · Higher
Đã giới thiệu| English | Ý nghĩa |
|---|---|
| time series/taɪm ˈsɪəriːz/ | dãy thời gian |
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.
- This lesson studies time series 时间序列: Measurements recorded in time order.
The method
- 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.
Why is a pie chart wrong for a time series of daily attendance?
Độ khó 1/5 · 100 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
A time series needs time on an axis so trend and pattern are visible. A pie chart shows shares of one total and discards the time order entirely.
A worked case
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.
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
10/40×360=90°.
Where it goes wrong
- 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.
Not true: A line graph is the best display for unrelated categories. Unrelated categories suit a bar chart; a line graph suggests a continuous change, such as over time.
Find pie angle for 15 of 40.
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
15/40×360=135°.
A line graph is the best display for unrelated categories.
Độ khó 1/5 · 100 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
Unrelated categories suit a bar chart; a line graph suggests a continuous change, such as over time.
Applying it
- 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.
Find pictogram symbols for 10 students if each represents 4.
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
10/4=2.5 symbols.
Match each display to the data it suits.
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
The display must match the structure of the data; pie angles are frequency/total×360° and a pictogram needs its key stated.
In your course
- AQA GCSE Mathematics (8300), Higher tier, specification section 3.6.
- Paper 1 is non-calculator: keep fractions, surds and π exact and show each step. On calculator papers, still write the expression before its value.
- Time series: Measurements recorded in time order.
- Use separate bars for categories, vertical line charts for discrete numerical values and time-ordered lines for a time series.
- Watch for: A pie chart must represent a complete total with non-overlapping categories.