Collecting and classifying dataIB MYP Maths Extended: Revision notes

Categorical data are described in words or categories, such as bag colour or favourite sport. Numerical data are numbers and are either discrete or continuous.

• Discrete data can only take separate values, usually found by counting: number of siblings, goals scored, shoe size.
• Continuous data can take any value in a range, usually found by measuring: height, mass, time. Continuous data are always rounded when recorded, but the true value could be anywhere in a range.

The population is every person or item you want to know about. A sample is a smaller group chosen from the population. A census asks the whole population, but this is often too slow or expensive, so we use a sample. A good sample is representative, meaning it has the same mix of people as the population. A larger sample is usually more reliable.

• Simple random: every member has an equal chance of being chosen (random numbers or a draw).
• Systematic: choose every $k$th member from a list, starting at a random point. For $600$ students and a sample of $30$, choose every $20$th.
• Stratified: split the population into groups (strata) and take a random sample from each in proportion to its size.
• Convenience: choose people who are easy to reach. This is quick but often biased. Stratified example: $120$ from $2\,400$ members, of whom $1\,500$ are adults: $\frac{1\,500}{2\,400}\times120=75$ adults.

Bias means the results are pushed in one direction, so they do not truthfully represent the population. It can come from:

• a sample that is not representative (only asking people at one place);
• self-selection, where volunteers take part, such as an online poll;
• non-response, where many people chosen do not reply, so the replies may be different from the rest;
• leading questions that suggest a particular answer. To reduce bias, use a random or stratified sample, a larger sample and neutral questions, and follow up non-responders.

A good question is clear, neutral and gives a time period ("each school day"). Answer boxes should cover every possible answer, not overlap, and be easy to tick: None; Less than 1 hour; 1 to less than 2 hours; 2 hours or more. Include "none" or "other" where it is needed. Do not ask two questions in one. Primary data are collected by you (survey, observation, experiment); secondary data were collected by someone else (a database or website). Use a tally chart to record counts as you go. A short pilot survey with a few people shows up unclear questions before the real survey.