Measures of Dispersion for Grouped Data · 7.2.5
Statistical mini-project
Students plan and carry out a small statistical investigation from start to finish: posing a statistical question, collecting real data, organising it into a table, representing it graphically, analysing it using an appropriate measure of central tendency and dispersion, then writing a clear description and conclusion that answers the original question.
The official learning standard (7.2.5)
“Design and conduct a mini-project involving statistical investigations based on measures of central tendency and measures of dispersion, and interpret and communicate the research findings. The report should include: (i) statistical questions, (ii) the data collection method, (iii) the data organisation method, (iv) graphical representations, (v) data analysis, and (vi) a related description and conclusion.”
What it means
Students plan and carry out a small statistical investigation from start to finish: posing a statistical question, collecting real data, organising it into a table, representing it graphically, analysing it using an appropriate measure of central tendency and dispersion, then writing a clear description and conclusion that answers the original question.
How it is examined
This standard is mainly developed through classroom-based project work rather than a single timed exam question. A related item in Paper 2 may ask students to state a suitable statistical question, suggest a data collection or organisation method, or identify which measure of central tendency and dispersion best suits a given investigation, without requiring a full project write-up.
Worked example
A class wants to investigate whether Form 5 students spend more time on their phones on weekdays or on weekends. Outline the mini-project by stating (a) a statistical question, (b) a suitable data collection method, (c) how the data should be organised, and (d) which measures of central tendency and dispersion would best analyse the results.
- (a) Statistical question: 'Is there a difference between the median daily phone usage time of Form 5 students on weekdays compared to weekends?'
- (b) Data collection method: distribute a short survey asking a representative sample of Form 5 students to record their phone usage time (in minutes) on one typical weekday and one typical weekend day.
- (c) Data organisation: record the weekday times and weekend times as two separate grouped frequency tables, using suitable class intervals (e.g. every 30 minutes).
- (d) Analysis: find the median and interquartile range (or the mean and standard deviation) for each set, since these summarise the typical usage time and how consistent it is, then compare the two sets to see which is higher or more varied.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What exactly counts as a 'statistical question' for the mini-project?
A statistical question is one that can only be answered by collecting and analysing data that varies from person to person or over time, such as 'Do Form 5 students who exercise more score higher marks?' It is not a question with a single fixed answer, like 'How many students are in this class?'
Which measures should I choose for the analysis section?
Choose a measure of central tendency (mean, median or mode) together with a matching measure of dispersion (range, interquartile range, variance or standard deviation), for example, median with interquartile range if the data has extreme values, or mean with standard deviation for more typical, evenly spread data.
What should the final conclusion of the report contain?
It should directly answer the statistical question posed at the start, referring back to the actual values calculated, for example stating which group had the higher median and whether one group's data was more spread out, rather than simply repeating the raw data or restating the question.