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.
Also known as: stem and leaf plot · tally chart · frequency table · data handling
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, and reading the mode, median and range off a display; the mean and the full summary come in the next lesson.
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 cannot be trusted to represent the whole school. A biased sample misleads you 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.
6Reading the mode, median and range off a display
Once data is organised, three summaries can be read straight off the display. The mode is the value that occurs most often. The median is the middle value once the values are in order (with an even number of values, it is halfway between the two middle ones). The range is the largest value minus the smallest. An outlier is a value that lies far away from the rest of the data.
- 1There are 9 values, so the median is the 5th value: 38.A stem-and-leaf display is already in order — count in from either end.
- 2Range = 51 − 23 = 28.Largest minus smallest.
- 3No value occurs more than once, so this data has no mode.A mode must occur more often than the other values.
7Grouping 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 they are normally the same width. Writing 0–10, 10–20 is wrong because 10 belongs to both.
8Double bar graphs
An ordinary bar graph shows one group. A double bar graph puts two groups side by side in each category, so you can compare them at a glance.
- The two bars in a pair touch; the gap goes between the categories.
- A key (legend) is not optional — without it nobody can tell which bar is which, and it carries a mark.
- Both groups share one vertical scale, which is the whole point: differences are read by comparing heights directly.
- 1Netball: girls 14, boys 4.Read each bar against the vertical scale.
- 214 − 4 = 10 more girls play netball.
- 3Athletics: boys 8, girls 9 — a difference of only 1.
- 4So athletics is the most evenly split.The smallest gap between the pair of bars.
9Pie charts
A pie chart shows how a whole is divided up. It answers “what share of the total?” rather than “how many?”
- 1Maths: 14/40 × 360° = 126°Frequency over total, times 360°.
- 2English: 10/40 × 360° = 90°
- 3Science: 10/40 × 360° = 90°
- 4Other: 6/40 × 360° = 54°
- 5Check: 126 + 90 + 90 + 54 = 360° ✓If the angles do not total 360°, something is wrong — do this before you draw.
Choose the right picture for the question. A bar graph compares amounts; a double bar graph compares two groups; a pie chart shows shares of one whole; a histogram shows grouped continuous data.
Drawing a pie chart when the categories do not make up a single whole. If learners could choose more than one sport, the totals overlap and a pie chart is meaningless — use a bar graph instead.
Practice exercises
Work each one out, then click to reveal the answer.
- 1In a survey of 60 learners, 15 chose soccer as their favourite sport. Calculate the size of the soccer sector in a pie chart of the results.
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15/60 of the learners chose soccer (1)
15/60 × 360° (1)
= 90° (1) - 2Is 'What is my height?' a statistical question? Why?
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No — there is only one answer. A statistical question must have answers that vary. - 3Define a population in statistics.
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The entire group being studied. - 4Why do we use a sample instead of the whole population?
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It is faster and cheaper; asking everyone is usually impractical. - 5You survey only your friends about school food. What is wrong?
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The sample is biased — it is not representative of the whole school. - 6What is wrong with the options '0–10, 10–20, 20–30'?
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They overlap — 10 and 20 each fit two intervals. - 7In a stem-and-leaf display, what value is stem 4 with leaf 7?
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47 - 8Data: 12, 15, 21, 24, 28, 33. Write the stems.
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Stems 1, 2, 3 (leaves: 2,5 | 1,4,8 | 3) - 9Tallies |||| |||| || represent what frequency?
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12 - 10In a survey of 60 learners, 25 chose soccer. Calculate the angle of the soccer sector in a pie chart.
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25/60 × 360° ✓✓ = 150° ✓ - 11A pie chart of 90 learners has sectors of 120°, 100°, 80° and x. Calculate x and the number of learners it represents.
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x = 360° − (120 + 100 + 80) = 60° ✓✓; 60/360 × 90 = 15 learners ✓ - 12State TWO features a double bar graph must have.
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A key/legend showing what each colour means ✓; one shared vertical scale for both groups, with the pair of bars touching and gaps between categories ✓ - 13Why would a pie chart be the WRONG choice for data where learners could pick more than one sport?
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The categories then overlap and do not add up to one whole ✓; a pie chart can only show parts of a single total, so a bar graph should be used ✓
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.