AC9M7ST03 • Homework
Statistical Investigations
Plan, collect, analyse, interpret and report. Use statistics to support conclusions and state limitations clearly.
Part A — Short response
- Write one clear statistical question that compares two groups using a measurable numerical variable. (2)
- Classify reaction time as discrete or continuous data and justify. (2)
- State one measure of centre and one measure of spread that could be used to compare two groups. (2)
- What does a long right tail in a distribution suggest? (2)
- State one limitation that should be reported in a school statistical investigation. (2)
Part B — Extended response
- Plan an investigation comparing reaction times for two groups. State the question, variable, data type, collection method and two ways you would make the comparison fair. (5)
- Group A reaction times (s): 0.40,0.42,0.43,0.44,0.45. Group B: 0.39,0.41,0.44,0.47,0.70. Compare centre, spread and any unusual value, then write a cautious conclusion. (5)
- A robot design is tested before and after modification. Before: median time 18 s, range 7 s. After: median 15 s, range 4 s. Interpret the result and state one limitation that could weaken the conclusion. (5)
- A published survey reports percentages for two groups. Explain four things you should check before making a conclusion from this secondary data. (5)
- Explain why a complete report should include the investigation question, data collection method, summary statistics, distribution shape, conclusion and limitations. (5)
Part C — Enrichment
11. Complete investigation design. Design a small statistical investigation about a measurable school or STEM question. Include: question, population/sample, variable and data type, collection procedure, suitable display, measures of centre/spread, how you would inspect shape and anomalies, the form of a justified conclusion, and at least two limitations.
Answers / marking guide
1
Answers vary. It should identify groups and a numerical variable, for example: “Do Group A students have lower reaction times than Group B students?”
2
Continuous, because time is measured and can take values throughout an interval.
3
Examples: mean or median for centre; range for spread.
4
It suggests a right-skewed distribution, often with some unusually high observations.
5
Examples include small/unrepresentative sample, measurement error, inconsistent conditions, nonresponse or limited precision.
6
A strong answer states a measurable question, reaction time as continuous data, a consistent method/device, similar testing conditions and enough repeated observations.
7
A median=0.43, range=0.05. B median=0.44, range=0.31, with 0.70 unusually high. A is slightly faster typically and much more consistent by range in this sample.
8
Lower median and lower range after modification suggest faster and more consistent performance. Limitations could include practice effect, different testing conditions, small sample size or measurement error.
9
Check source, sample/population, sample size/response rate, question wording/method, dates, variable definitions and limitations. Conclusions should remain at the level supported by the survey.
10
Each component supports a different stage of the investigation: purpose, evidence quality, numerical description, distribution interpretation, answer to the question and limits on confidence/generalisation.
11
Responses vary. Full-credit work should show a coherent investigation cycle and connect the conclusion directly to the collected evidence while acknowledging limitations.