Lesson 25: Data Collection and Organisation

§Text Passage

1Summary 重點摘要

Statistics is collecting, organising, analysing data. Use frequency table to organise data. Learn to do surveys and frequency tables.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Block 1: Do a SurveyTo find out classmates' preferences, step one is designing a clear question, such as 'Which subject do you like most?', and then collecting answers from the whole class; every answer gathered is a piece of data. Why must the question be clear? Because a vague question produces answers that cannot be sorted, and the statistics never start; a question like 'How do you feel about school?' scatters too widely to classify. The answer options must be definite as well, so that everyone can reply with ease. A common error is a leading question, such as 'Maths is fun, so is Maths your favourite?', which yields unreliable data and defeats the survey.
2. Block 2: CategoriseCollected data must be sorted into categories: for favourite subjects, set up categories such as Maths, Chinese, English and General Studies, and place every answer into its own category. Why must the sorting standard be consistent? Because one answer may go into one category only; if the standard wavers, with some filing Science under General Studies and others under Others, the results become muddled and unreliable. Settle the categories before sorting begins, adding an 'Others' item when needed for hard-to-place answers. A common error is overlapping categories, such as keeping both 'Chinese' and 'Language'; categories must not overlap, yet together must cover every answer.
3. Block 3: Count FrequenciesTo count how many fall in each category, tally marks are the usual tool: one stroke stands for 1, and a completed tally group stands for 5. For example, 5 pupils choosing Maths is drawn as one full tally group; 6 pupils is a full group plus one more stroke. Why the tally? Because five strokes to a group lets the amount be estimated at a glance, and ticking along while listening is quick, far easier than writing digits one by one. A common error is a misplaced or doubled stroke when answers come fast; if a stroke is missed, recheck the original answers rather than guessing, since accuracy of the data always comes first.
4. Block 4: Make Frequency TableFill the sorted results into a table: one row lists the categories, the subject names; the other lists the frequencies, the headcounts. The table needs a title above it stating what was surveyed, such as 'P6 Pupils' Favourite Subjects Survey'. Why is the frequency table a required step before drawing any chart? Because it turns scattered raw data into a tidy overview where every category's size is plain, and drawing then takes numbers straight from the table with little room for error. A common error is omitting the title, or mismatching categories with frequencies; after making the table, check cell by cell that every frequency sits against its own category.
5. Block 5: Pie Chart (Intro)A frequency table can be drawn as a pie chart: the whole circle stands for all the data, and each category takes a share of the angles. For example, in a class of 20, the 5 pupils who like Maths most hold a share of 520 = 14, drawn as an angle of 14 × 360° = 90°. Why is the angle in proportion to the frequency? Because the pie chart allocates the whole by angle: the larger the frequency, the larger the angle; with 20 pupils matching 360°, each pupil is worth exactly 18°, and the count times 18° gives the angle. A common error is using the frequency as the angle directly, skipping the division by the total; the order is always share first, then multiply by 360°.
6. Block 6: Bar ChartA bar chart uses the lengths of bars to show frequencies: the longer the bar, the larger the number; the shorter, the smaller. Categories go on the horizontal axis, numbers on the vertical axis, and the scale must be labelled. Why does the bar chart suit comparisons? Because the bars stand side by side, letting the largest and the smallest be seen at a glance — the tallest bar marks the most popular subject. It divides work with the pie chart: comparisons use bars, proportions use the circle. A common error is bars of unequal widths, or a missing scale, which makes accurate comparison impossible; draw neatly, keep every bar the same width, and space them evenly.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Statistics = collect + organise + analyse
• Frequency = how many per category
• Frequency table: category + frequency
• Pie chart total 360°
• Bar chart uses bar length