What is a statistical inquiry?
A statistical inquiry (also called a statistical investigation) is a way to answer a question using data. It is a cycle with five steps, often called PPDAC:
- Problem – write a question that data can answer.
- Plan – decide what to measure, who to ask and how.
- Data – collect, record and clean the data.
- Analysis – sort, graph and summarise it.
- Conclusion – answer the question and say how sure you are.
A good statistical question expects answers that vary. “How tall am I?” is not statistical (one answer). “How tall are students in Class 8?” is statistical (many different answers).
Planning: population, sample and variables
The population is everyone (or everything) the question is about. Asking everyone is a census. Usually we ask a sample, a smaller group. A fair sample is random: every member has the same chance of being picked.
A variable is what we measure. It can be categorical (bus, walk, car) or numerical (time in minutes, height in cm). Plan the exact question wording, answer choices, units and how you will record answers (tally chart, spreadsheet).
Primary and secondary data
Primary data you collect yourself (survey, experiment, observation). Secondary data someone else collected (census tables, weather records, websites).
Collecting data and analysing it (with ICT)
Record each answer straight away. Check for mistakes such as a height of 1,500 cm (should be 150 cm). Then organise the data in a frequency table.
Choose a graph that fits: bar chart or pie chart for categories, histogram or dot plot for numbers, line graph for change over time. Find a centre (mean, median or mode) and a spread (range).
A spreadsheet saves time: type the data in one column, use functions such as AVERAGE, MEDIAN, MAX, MIN and COUNTIF, and insert a chart. Free tools and graphing apps do the same.
Conclusions and critiquing a study
A conclusion answers the original question in words and numbers: “About 40% of students in our sample walk; walking is the most common way.”
Then critique it – yours or anyone’s (news, adverts):
- Was the sample big enough and random?
- Was there bias? Asking only students at the bus stop would give too many bus users.
- Was the question leading? (“Don’t you agree walking is healthy?”)
- Can the result be generalised to other schools or seasons?
Good inquiries end with a new question, so the cycle goes round again.
Key formulas and definitions
- PPDAC: Problem → Plan → Data → Analysis → Conclusion
- Population: the whole group the question is about
- Sample: the part of the population that is studied
- Census: data collected from every member of the population
- Variable: a quantity or quality that can vary (categorical or numerical)
- Bias: a fault in the method that pushes results one way
- Percentage = (frequency ÷ total) × 100
Worked examples
1. Is “What is the weight of my school bag?” a statistical question? Rewrite it if not.
No – it has only one answer. A statistical version: “What is the typical weight of school bags carried by Class 8 students in our school?” This expects many different answers that vary.
2. In a survey of 40 students, 14 chose football, 10 cricket, 9 basketball and 7 badminton. Give the percentage for each and the mode.
Football 14/40 × 100 = 35%; cricket 25%; basketball 22.5%; badminton 17.5%. Check: 35 + 25 + 22.5 + 17.5 = 100%. The mode is football.
3. A newspaper asked 200 people outside a gym whether they exercise daily; 80% said yes. It reported “80% of the city exercises daily”. Critique this.
The sample is biased: people outside a gym exercise more than average, so they do not represent the whole city. The sample is not random. A fair method would pick people at random from the whole city (e.g. from voter or address lists), so the 80% figure cannot be generalised.
Common mistakes
- Asking a question with only one answer – that is not a statistical question.
- Taking a convenient sample (friends, one class) and calling it random.
- Writing a leading question that pushes people towards one answer.
- Stating a conclusion for a bigger group than the sample really represents.