Data handling turns a question into evidence: define the group of interest, collect relevant observations, classify them, record frequencies and interpret the results. Categories describe types; numerical data measure or count quantities. A representative sample should reflect the population, not only the easiest people to ask. Discrete numerical data take separate countable values, such as number of siblings. Continuous numerical data can take any value within an interval, such as height or elapsed time, even when measurement rounds the recorded value. Organise categories or classes so that each observation is counted once. **Display** | **Useful for** | **Limitation to remember** Frequency table | Exact counts by value or category | Patterns may be less immediate than in a graph. Bar graph | Comparing categories; separate bars | Check the baseline and equal bar widths. Pictogram | A quick visual comparison | Read the key; a partial symbol represents part of its value. Line graph | Changes over ordered times | Joining categories without meaningful order can mislead. Pie chart | Parts of one whole | Harder to compare small differences or different sample sizes. Example A travel survey records bus 12, walk 8, car 4, total 24. A pictogram key of one symbol for four pupils requires three, two and one symbols. The bus sector in a pie chart is 1224 x 360 =180. Asking only pupils at the bus stop would bias this survey towards bus users. A bar axis beginning at 7 makes counts 8 and 12 appear much more different than their actual ratio 12:8. Describe the scale distortion, not merely that the chart “looks wrong”.

Collecting data and choosing a display

TGM Original — E Math Summary Notes (4052), 2026 editorial manuscript

Data handling turns a question into evidence: define the group of interest, collect relevant observations, classify them, record frequencies and interpret the results. Categories describe types; numerical data measure or count quantities. A representative sample should reflect the population, not only the easiest people to ask.

Discrete numerical data take separate countable values, such as number of siblings. Continuous numerical data can take any value within an interval, such as height or elapsed time, even when measurement rounds the recorded value. Organise categories or classes so that each observation is counted once.

Display	Useful for	Limitation to remember
Frequency table	Exact counts by value or category	Patterns may be less immediate than in a graph.
Bar graph	Comparing categories; separate bars	Check the baseline and equal bar widths.
Pictogram	A quick visual comparison	Read the key; a partial symbol represents part of its value.
Line graph	Changes over ordered times	Joining categories without meaningful order can mislead.
Pie chart	Parts of one whole	Harder to compare small differences or different sample sizes.

Example

A travel survey records bus \(12\), walk \(8\), car \(4\), total \(24\). A pictogram key of one symbol for four pupils requires three, two and one symbols. The bus sector in a pie chart is \(\dfrac{12}{24}\times360^\circ=180^\circ\).

Asking only pupils at the bus stop would bias this survey towards bus users. A bar axis beginning at \(7\) makes counts \(8\) and \(12\) appear much more different than their actual ratio \(12:8\). Describe the scale distortion, not merely that the chart “looks wrong”.

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