How do you tell which average or spread measure actually makes sense?
You can wreck a statistics question before you even calculate anything if you pick the wrong tool for the data. If your data is labels like bus, bike, or walk, averaging is nonsense. If your data is numbers, then averages and spread measures can tell you where the data sits and how much it varies.
Univariate data means you are tracking just one variable for each person or item, like one test score per student or one temperature per day.
Distribution is the overall look of your data set: where the middle seems to be, how stretched out it is, whether it leans to one side, and whether there are gaps or unusual values.
You’ll usually sort data first because messy raw values hide patterns. Once the values are in order, it becomes much easier to spot the middle, the spread, and anything strange.
After that, classify the data. Categorical or qualitative data gives you groups or names. Numerical or quantitative data gives you values you can calculate with. Numerical data then splits again into discrete data, which comes from counting, and continuous data, which comes from measuring.
Categorical / qualitative data puts results into named groups rather than number values.
Numerical / quantitative data records values as numbers, so you can use measures such as mean, median, quartiles, and standard deviation.
Discrete data takes separate countable values, usually whole numbers.
Continuous data can take any value in an interval, even if you rounded it when recording.
A sneaky mistake: if someone’s height is written as 162 cm, that does not make height discrete. Height is still continuous; you just recorded it to the nearest centimetre.
When values repeat a lot, a frequency table saves time by showing how often each value appears. If the data covers many possible values, especially continuous data, you often group it into intervals.
A grouped frequency table collects values into class intervals and records how many fall in each interval.
Grouped data is efficient, but there’s a trade-off: once values are bundled into intervals, you lose the exact original numbers. That matters later, because some statistics become estimates instead of exact answers.
How can you organise data without losing the actual values?
If you want a display that shows shape and keeps every original number visible, use a stem-and-leaf diagram. It’s like splitting each value into a front part and an end part, so your data becomes easier to scan without turning into a blur of digits.
A stem-and-leaf diagram arranges numerical data by separating each value into a stem and a leaf, so you can still rebuild the original values.
The stem is the leading digit or digits, and the leaf is the final digit. The place value has to stay consistent all the way through, or the diagram becomes misleading.
Method: building a stem-and-leaf diagram
- Put your data in ascending order.
- Decide what the stem and leaf will represent.
- Write the stems in a vertical list.
- Add each leaf beside the correct stem.
- Order the leaves from smallest to largest on each row.
- Include a key so the reader knows the place value.
Worked example
Suppose your data is: 10, 12, 14, 15, 18, 21, 23, 23, 27.
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Use the tens digit as the stem and the ones digit as the leaf.
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Write the stems 1 and 2.
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Place each value:
- 10 → 1 | 0
- 12 → 1 | 2
- 14 → 1 | 4
- 15 → 1 | 5
- 18 → 1 | 8
- 21 → 2 | 1
- 23 → 2 | 3
- 23 → 2 | 3
- 27 → 2 | 7
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Final diagram:
1 | 0 2 4 5 8
2 | 1 3 3 7 -
Key: 1 | 0 = 10
That key matters more than students think. Without it, your reader can’t tell whether 1 | 0 means 10, 1.0, 100, or something else.
If your data is grouped into intervals instead, you can’t recover the exact original values. That’s the big difference between grouped tables and stem-and-leaf diagrams.
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