Qualitative data is non-numerical — categories like favourite colour or mode of transport. Quantitative data is numerical, and splits further into:

• Discrete — only specific, countable values (number of siblings; you can't have $2.5$ of them).
• Continuous — any value within a range, limited only by how precisely it's measured (height, time, mass).

Ask: "could the value fall strictly between two listed values?" Shoe sizes look measurement-like, but they jump in fixed steps ($6, 6.5, 7, \dots$) with nothing valid in between — so shoe size is discrete, not continuous, despite appearances. Money is a similar trap: amounts look continuous, but because the smallest unit is a fixed amount (e.g. $1$ cent) with nothing smaller in between, it behaves as discrete data in practice.

Tally marks are grouped in fives (four vertical strokes, the fifth struck through) so large totals can be counted quickly and accurately by eye.

Example: the number of pets owned by $20$ households is recorded as they're surveyed: $0,1,2,1,0,3,1,2,1,0,2,1,1,0,3,2,1,0,1,2$. Tallying each value as it's encountered, then totalling:

Converting a raw, unordered list into a tally table like this is almost always the first step before any average, chart or diagram can be produced — it's worth doing carefully, since an error here carries through every later calculation.

A two-way table cross-classifies data by two categories at once, with row and column totals that must agree however they're checked.

Example: $50$ students were asked whether they walk or cycle to school. $28$ walk, of whom $16$ are girls; $22$ students in total are boys.

Working: total cycle $=50-28=22$; total girls $=50-22=28$; girls who cycle $=28-16=12$; boys who walk $=28-16=12$; boys who cycle $=22-12=10$.

Continuous data (like heights or times) is almost always grouped into equal-width class intervals before being tabulated, since listing every individual measured value separately would be unmanageable. A good choice of intervals is wide enough to give roughly $5$–$10$ classes overall, but not so wide that most of the detail in the distribution is lost.

Example: the heights (in cm) of $40$ plants range from $12$ cm to $58$ cm. A sensible set of class intervals might be $10<h\le20$, $20<h\le30$, $30<h\le40$, $40<h\le50$, $50<h\le60$ — five equal-width classes covering the full range without gaps or overlaps. Writing boundaries with a strict inequality on one side (as here) avoids any value being ambiguous about which class it belongs to.