Collecting and Organising Data

Before organising data into bigger tables, make sure the data types are clear — they decide which table to use.

• Categorical data uses words or groups, such as favourite sport or eye colour.
• Numerical data is made of numbers. It splits again into two kinds.
• Discrete data is counted in separate steps — number of siblings, goals scored.
• Continuous data is measured and can take any value — height, mass, time.

This matters because continuous data almost always needs to be grouped — you cannot have a separate row for every possible height. That is exactly what a grouped frequency table is for, and it is the first new idea this year.

Good data starts with good planning. Once you have a precise statistical question, work through these decisions:

• What to record — the single piece of information that answers your question.
• How to collect it — a survey, a questionnaire, a measurement or an observation.
• Who to include — the group you collect from is your sample.
• How to keep it fair — everyone in the sample should have an equal chance of being chosen.

A sample is used because asking everyone (the whole population) is usually impossible. But a sample only works if it represents the population. Asking only your friends, or only one class, gives a biased result.

A larger, fairly chosen sample gives more reliable results. A tiny or one-sided sample can make your answer to the question completely misleading.

When numerical data has lots of different values — like 30 students' heights — a row for every value would be huge. Instead you sort the data into groups, called class intervals, in a grouped frequency table.

Each class interval covers a range of values. Two rules make the groups work:

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

Notice the neat way the groups are written: $150 \le h < 160$ means "150 up to but not including 160". A student exactly 160 cm tall goes in the next group. Keeping the class intervals the same width (here, 10 cm) makes the table fair and easy to draw a chart from.

Grouping has a cost: once data is grouped you lose the exact values. You know 8 students are between 150 and 160 cm, but not their precise heights.

Sometimes you want to record two things about each person — say, their year group and whether they walk or cycle to school. A two-way table does exactly that, with one variable down the rows and the other across the columns.

The power of a two-way table is the totals. Add across each row, add down each column, and the row totals and column totals must both add up to the same grand total (here, 40). That gives you a built-in check, and lets you fill in a missing cell.

To read the table, find where a row meets a column. The Year 7 row meets the Cycle column at 6, so 6 Year 7 students cycle.

Organising data well is a balance. The aim is to make data easy to understand without hiding anything important.

Think carefully about your class intervals:

• Too few, wide groups — the table is short, but you lose detail and patterns disappear.
• Too many, narrow groups — you keep detail, but the table becomes long and hard to read.
• A sensible choice is usually five or six equal groups.

The same honesty applies to two-way tables — always include the totals, so a reader can check the figures and trust them. Tidy, well-chosen tables make the next steps — drawing charts and finding averages — far easier.

Grouped frequency tables and two-way tables are tools you will reach for constantly:

• Data representation — a grouped frequency table is exactly what you need to draw a frequency diagram, and two-way tables feed comparative bar charts.
• Averages and range — you will estimate averages from grouped data and read frequencies straight from these tables.
• Probability — a two-way table is a clear way to find probabilities involving two events at once.
• In science and geography, you will record measurements in grouped tables and survey results in two-way tables all the time.

Whenever you see a neat table of results — a weather record, a survey summary — remember it began with someone planning carefully, choosing sensible groups, and organising the data so it stayed honest and clear.