Running a data investigation properly — samples and bias, grouping data into class intervals, drawing and reading histograms, and choosing between the mean, median and mode when the data has outliers.
Grade 9 data handling is less about calculating and more about judgement: is this sample fair, are these intervals sensible, and is the mean actually the right summary to use?
1Samples, populations and bias
The population is everyone you want to know about; the sample is the part you actually ask. A sample is only useful if it is representative.
- Random sample — everyone has an equal chance of being picked. Usually the fairest.
- Biased sample — some group is over-represented, so the results are misleading.
Surveying shoppers outside a sports shop about "how often do you exercise?" gives a badly biased answer — the location itself selects sporty people. Always ask where and who before trusting a statistic.
2Grouping data into class intervals
With many different values, group them into equal, non-overlapping class intervals such as 0–9, 10–19, 20–29. You lose the individual values but the pattern becomes visible.
Intervals must be equal in width and must not overlap. Writing 0–10, 10–20 is wrong — 10 belongs to both.
3Histograms
A histogram shows grouped numerical data. Its bars touch, because the classes are continuous. A bar graph shows separate categories, so its bars have gaps between them.
- 1The tallest bar is 20–29 with a frequency of 9.The modal class is the interval with the highest frequency.
- 2Total = 3 + 7 + 9 + 5 + 2.Add every frequency.
- 3Total = 26 values.
4Pie charts
A pie chart shows how a whole splits into parts. Each slice’s angle is that category’s share of the total, out of 360°.
Always check that your slice angles add up to 360° — it catches arithmetic slips instantly.
5Choosing the right average
- Mean — uses every value, but a single extreme value drags it badly.
- Median — the middle value; barely affected by outliers, so it is safer for skewed data.
- Mode — the most common value; the only average that works for categories like favourite colour.
- 1Mean = 116 500 ÷ 5 = R23 300.But nobody earns near that — the R80 000 distorts it.
- 2Median = R9 500.The middle value once ordered.
- 3The median is the fairer summary here.One outlier has pulled the mean far above almost everyone.
If a data set has an obvious outlier, expect the exam to ask which average is more appropriate — the answer is nearly always the median, and you must say why.
Practice exercises
Work each one out, then click to reveal the answer.
- 1What is the difference between a population and a sample?
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The population is the whole group; the sample is the smaller part actually surveyed. - 2Why is surveying only your friends about school food biased?
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They are not representative of the whole school. - 3What is wrong with the intervals 0–10, 10–20, 20–30?
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They overlap — 10 and 20 each fit two intervals. - 4How do a histogram and a bar graph differ?
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Histogram bars touch (continuous data); bar-graph bars have gaps (separate categories). - 5In the histogram above, which is the modal class?
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20–29, with a frequency of 9 - 6In the histogram above, how many values are there in total?
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3+7+9+5+2 = 26 - 7Find the mean of R8 000, R9 000, R9 500, R10 000 and R80 000.
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116 500 ÷ 5 = R23 300 - 8Find the median of that same salary data.
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R9 500 - 9Which average is fairer for that salary data, and why?
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The median — the R80 000 outlier pulls the mean far above what almost everyone earns.
Quick Quiz
5 quick questions on what you just read. Take it when you feel ready.
Now practise it
Download Grade 9 past papers and worksheets on this topic.