Collecting and Organising Data

Last year you learned to plan a single data collection. This year you see the whole picture: a data project is a cycle of clear stages, and collecting and organising data are the first two.

The two stages you focus on this year are the ones where things most easily go wrong:

• Collect — get the data without introducing bias.
• Organise — sort the data into clear tables that do not mislead.

Get these two right and the later analysis can be trusted. Get them wrong and no clever calculation can rescue the project. The rest of this guide shows you how to keep both stages fair.

You usually cannot ask the whole population, so you study a sample. But a sample is only useful if it represents the population — its mix of people should reflect the bigger group.

Two things make a sample trustworthy:

• Size — a tiny sample is easily swayed by chance. A larger sample is more reliable.
• Selection — everyone in the population should have a fair chance of being chosen.

A random sample — where every member has an equal chance of being picked — is the fairest method, because it removes human choice. Asking only friends, only one class, or only people who happen to walk past is not random, and the results will lean to one side.

Bias is anything that makes your data lean unfairly towards one kind of answer. A biased investigation gives a misleading conclusion even when the maths is perfect, so learning to spot bias is a key Stage 9 skill.

Three common sources of bias:

• A leading question — wording that nudges people towards an answer, like "Don't you agree our canteen food is poor?"
• A one-sided sample — choosing only a particular group, such as asking only sporty students about exercise.
• The time or place — surveying at the school gate at 8 am misses everyone who arrives early or late.

To reduce bias, write neutral questions that do not hint at an answer, choose a sample that mirrors the whole population, and collect data at a range of times and places. A fair process protects every later step of the investigation.

Once data is being collected, you need a data collection sheet ready — usually a grouped frequency table with a tally column, so values can be recorded quickly and accurately.

Designing the class intervals well is the skill here. Two rules from last year still hold:

• No overlaps — every value must fit exactly one class.
• No gaps — every possible value must fit some class.

And keep every class interval the same width.

Write classes the neat way: $5 \le m < 10$ means "5 up to but not including 10", so a value of exactly 10 goes in the next class. A well-designed sheet makes recording fast and stops the same value being counted twice or missed.

A two-way table records two things about each person at once — say, year group and whether they have school lunch. This year you go further: using the totals to reason and fill in gaps.

There are two ways to find the missing cell. The Year 9 row must add to 25, so the blank is $25 - 9 = 16$. As a check, the Lunch column must add to 34, so the blank is $34 - 18 = 16$ too — and the two methods agree.

This is the power of a two-way table: the row totals and column totals both add to the grand total (55 here), giving you a built-in check and a way to recover any single missing value.

Planning fair samples and designing honest tables are skills you will keep using:

• Data representation — a grouped frequency table is exactly what you need to draw a frequency diagram, and two-way tables feed comparative charts.
• Averages and range — grouped tables are the data sets you summarise with an estimated mean and a modal class.
• Probability — a two-way table is a neat way to organise outcomes and find probabilities involving two events.
• IGCSE and beyond — sampling, bias and questionnaire design appear again, and in science you will design fair experiments using exactly this thinking.

Whenever you read a survey result in the news, you now know the questions to ask: who was sampled, how, and could the wording have nudged the answers? That is what it means to think like a statistician.