0580 · 9.1Classifying statistical data

Types and classification of data

0:00Imagine collecting lunch choices from a whole class. Individual answers tell you what each student chose, but a table makes the overall counts easier to find. Organising those answers carefully is the first step in using statistics. In this video, you will learn to classify data, construct tally tables, and complete two-way tables. Data are pieces of information collected about people, objects, or events. Each recorded answer or measurement is an observation.

0:25To classify data means to sort observations into categories according to their characteristics. To tabulate data means to organise them in a table with clearly labelled rows and columns. Qualitative data describe categories, such as a lunch choice or favourite colour. Quantitative data are numerical, such as the number of siblings or a measured height. Discrete data take only separate values, often from counting, and shoe size is discrete too.

0:49Continuous data are measured and can take any value within a range, such as height, time or mass. These distinctions help us choose sensible categories, but the central task is organising the observations accurately. Each observation must have an unambiguous place in the table. Categories should not overlap, and together they should cover all the possible answers. For this lesson, each student gives exactly one answer to each question.

Tally tables and two-way tables

1:13Our first worked example asks us to classify and tabulate the twelve lunch choices on the board. We create one row for each lunch category. Then we read through the answers in order, adding one tally mark to the matching row. Moving systematically through the list helps prevent omissions and double counting. Tallies are grouped in fives, with the fifth mark drawn diagonally across the previous four. A frequency is the number of observations in a category.

1:37Six baguette choices produce a group of five tallies and one extra mark. The other rows contain four wrap choices and two cooked meal choices. We add six, four and two to obtain a total frequency of twelve. This agrees with the number of original observations. The tally column records the counting process, while the frequency column gives the final count. Matching totals are a useful check, although they cannot reveal every possible classification error.

2:04A two-way table classifies the same observations using two characteristics at once. One characteristic determines the rows, and the other determines the columns. Each internal cell counts observations satisfying both its row heading and its column heading. The totals around the edges count everyone within a whole row or column. In our second example, twenty students are classified by year group and club attendance. Six students from year nine attend a club, so that number goes in the year nine row under attends club.

2:31The four non-attenders go in the neighbouring cell. For year ten, the corresponding entries are three attending and seven not attending. The year nine total is 6 + 4, giving ten. In the second row, 3 + 7 also gives ten. Down the attendance column, 6 + 3 gives nine club attenders. The non-attendance total is 4 + 7, which equals eleven. Adding the row totals gives twenty students altogether.

Completing two-way tables

2:57The column totals agree, because 9 + 11 makes the same grand total. These are two routes to the same grand total, not two separate groups of students. Adding both sets of totals together would count every student twice. An exam-style question may ask you to complete a partially filled two-way table. Here, thirty pupils are classified by group and lunch type. The junior group contains twelve pupils, and eight bring a packed lunch.

3:21We use the totals to find the missing counts, rather than guessing from the table’s appearance. Subtract eight from twelve to find four juniors having school meals. The packed lunch column totals ten, so subtracting the eight juniors leaves two seniors with packed lunches. Subtracting two from eighteen leaves sixteen seniors having school meals. Finally, 4 + 16 gives twenty school meals altogether. We check the grand total by adding ten and twenty to obtain thirty.

3:47Every missing entry is now supported by a row or column total. These counting and subtraction methods must work without a calculator on Paper Two. They also apply on calculator Paper Four, and frequencies remain exact whole numbers without rounding. Common mistakes include confusing an internal cell with a total and placing a count under the wrong heading. Eight here means juniors with packed lunches, not all juniors or everyone with packed lunches.

4:12Read both headings before interpreting an internal cell. Also remember that an empty cell is unknown, whereas a written zero means no observations. The key idea is that classification gives each observation a clear place, while tabulation makes the counts accessible. Tally tables organise counts using one characteristic. Two-way tables use two characteristics together, with totals linking their cells. Clear headings, systematic counting, and consistent totals make your tables reliable.