How a statistics investigation actually works — asking a good question, samples versus populations, questionnaires, and organising results with tally tables, stem-and-leaf displays and grouped intervals, with a worked diagram and a quiz.
Data handling always follows the same cycle: ask a question → collect data → organise it → summarise it → draw a conclusion. This lesson covers the first three steps; summarising with the mean, median and mode comes next.
1Asking the question and choosing a source
A statistical question must have answers that vary. "How old am I?" is not a statistical question — there is one answer. "How old are the learners in Grade 8?" is, because the answers differ.
- Primary data — you collect it yourself (a survey, a measurement, an experiment).
- Secondary data — someone else collected it (newspapers, books, websites, Stats SA).
2Population versus sample
A sample is the smaller part of it that you actually ask.
Asking all 1 200 learners in a school takes too long, so you ask perhaps 60. For the results to be trustworthy the sample must be representative — it should look like the population in miniature.
Biased sample: if you want to know the favourite sport of a whole school but only ask the netball team, your results are useless. A biased sample gives a wrong answer no matter how carefully you do the maths afterwards.
3Designing a questionnaire
- Keep questions short and clear, with one idea per question.
- Give multiple-choice options that do not overlap and cover every possibility.
- Avoid leading questions that push people towards an answer.
Age options like "10–12, 12–14" overlap — a 12-year-old fits both. Use "10–12, 13–15" instead.
4Tally tables
A tally table records results as you collect them. Group tallies in fives (four strokes with the fifth crossing through) so they are quick to count.
- 1Soccer |||| |||| = 10, Netball |||| = 5, Rugby |||| ||| = 8.Count each set of five as a block.
- 2Frequency column: Soccer 10, Netball 5, Rugby 8.The frequency is simply how many times each answer occurred.
- 3Total = 23 learners.Always total the frequencies — it checks nothing was lost.
5Stem-and-leaf displays
A stem-and-leaf display organises numbers without losing any of them. The stem is the tens digit and the leaf is the units digit.
A stem-and-leaf display is really a sideways bar graph that still shows every single value — which is why you can read the median straight off it.
6Grouping data into intervals
When there are many different values, group them into equal class intervals such as 0–9, 10–19, 20–29. This makes patterns visible, but you can no longer see the individual values.
Intervals must never overlap and must be the same width. Writing 0–10, 10–20 is wrong because 10 belongs to both.
Practice exercises
Work each one out, then click to reveal the answer.
- 1Is 'What is my height?' a statistical question? Why?
Show answer ▾Hide answer ▴
No — there is only one answer. A statistical question must have answers that vary. - 2Define a population in statistics.
Show answer ▾Hide answer ▴
The entire group being studied. - 3Why do we use a sample instead of the whole population?
Show answer ▾Hide answer ▴
It is faster and cheaper; asking everyone is usually impractical. - 4You survey only your friends about school food. What is wrong?
Show answer ▾Hide answer ▴
The sample is biased — it is not representative of the whole school. - 5What is wrong with the options '0–10, 10–20, 20–30'?
Show answer ▾Hide answer ▴
They overlap — 10 and 20 each fit two intervals. - 6In a stem-and-leaf display, what value is stem 4 with leaf 6?
Show answer ▾Hide answer ▴
46 - 7Data: 12, 15, 21, 24, 28, 33. Write the stems.
Show answer ▾Hide answer ▴
Stems 1, 2, 3 (leaves: 2,5 | 1,4,8 | 3) - 8Tallies |||| |||| || represent what frequency?
Show answer ▾Hide answer ▴
12
Quick Quiz
4 quick questions on what you just read. Take it when you feel ready.
Now practise it
Download Grade 8 past papers and worksheets on this topic.