Classifying statistical data.
Identify the type of data and organise observations so every frequency can be checked.
Classify categorical, discrete and continuous data · use tally and two-way tables · choose clear class boundaries
Identify what the data describe
Data are recorded observations, such as each student’s journey time or favourite activity. A variable names the characteristic being recorded. Before calculating anything, ask what one observation represents.
Words such as a favourite colour form categories. Numerical counts such as siblings are discrete, while measured quantities such as height are continuous. A numerical-looking label is not automatically a measurement: a bus route number names a category rather than a count or size.
A variable is the characteristic recorded for each person or object. Its type helps you choose a sensible table, graph and average.
| Type | Meaning | Examples |
|---|---|---|
| Qualitative (categorical) | Labels or categories | Travel method; eye colour |
| Ordered categories | Categories with a meaningful order | Poor, satisfactory, good |
| Quantitative, discrete | Numerical values that can be counted | Number of siblings: 0, 1, 2, … |
| Quantitative, continuous | Numerical values measured on a scale | Height, mass, time |
Pause and explainIs a height rounded to a whole centimetre a discrete variable?
The underlying height is continuous. Rounding limits the recording precision but does not change the type of quantity measured.
Organise observations in a tally table
An unorganised list makes repeated values difficult to count reliably. A tally table gives each observation one place to go, and a frequency records how many observations belong there.
Choose categories before tallying and process the original list in order so no item is skipped or counted twice. Group tallies in fives for easy counting. Finally add the frequencies and compare with the number of original observations; the totals should match.
Use one tally for each observation. Group every fifth tally diagonally across the preceding four, then count to obtain the frequency.
| Method | Tally | Frequency |
|---|---|---|
| Bus | 7 | |
| Walk | 5 | |
| Cycle | 3 | |
| Car | 5 | |
| Total | 20 |
Use the travel table to identify the most common method and check the total.
Bus has the highest frequency, 7. The total frequency is 7 + 5 + 3 + 5 = 20, matching the number of observations.
Pause and explainWhy check the frequency total against the length of the original list?
A mismatch indicates that an observation was missed, repeated or classified incorrectly.
Use a two-way table for two classifications
One individual can be classified in two ways at once, such as year group and travel method. A two-way table keeps those classifications together rather than separating them into unrelated lists.
Read a cell as the intersection of its row and column labels. Marginal totals combine a whole row or column, and the grand total counts all individuals. A percentage about one year group uses that group’s total, while a whole-population percentage uses the grand total.
| Year group | Cycle | Bus | Total |
|---|---|---|---|
| Year 10 | 8 | 12 | 20 |
| Year 11 | 6 | 14 | 20 |
| Total | 14 | 26 | 40 |
How many Year 11 students cycle? How many students take the bus altogether?
The cell at Year 11 and Cycle gives 6. The Bus column total gives 26.
Out of Year 10, 8 of 20 cycle: 40%. Out of all students, 14 of 40 cycle: 35%. The denominator depends on the group named in the question.
Pause and explainWhy can two percentages using the same cell have different denominators?
They may refer to different groups, such as a row’s students versus all students in the table.
Your turn. Classify and tabulate.
Identify what each observation describes before naming its data type or creating categories. Check that every observation has exactly one intended place in a simple classification.
For two-way tables, read both labels before using a cell. Verify row, column and grand totals, then choose the denominator matching the population named in the question.
Classify shoe colour, number of goals and journey time.
Reveal worked answer
The values are 0, 1, 2, 1, 0, 3, 1, 2. Give their frequency distribution.
Reveal worked answer
In the two-way table, find the percentage of Year 11 students who take the bus.
Reveal worked answer
A row total is 35. Two of its three cells are 12 and 9. Find the missing cell.