Data Organization and Graphs

1Summary 重點摘要

Learn how to organize data, and common statistical graphs.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: The basic idea of statisticsStatistics is the study of collecting, organising, analysing and presenting data. To survey the heights of a class: measuring and recording each student is collection; grouping the heights into a table is organisation; computing the mean is analysis; drawing a chart to report to others is presentation. Why four stages? Raw data are chaotic, and only after processing do they become useful information. A common mistake is drawing conclusions from unorganised data, for example claiming the whole class is tall from a few high values.
2. Step 2: The frequency tableThe most basic way to organise data is a frequency table: group the data by category or interval and count how many fall in each group; the count is the frequency. For example, surveying favourite subjects gives Mathematics 10, Chinese 8, English 12 and Science 10, totalling 40, and each count is a frequency. Why does the table matter? It is the basis of every statistical chart, and each number on a chart comes from the table. A common mistake is a total of frequencies that does not match the number of data; check the sum after making the table.
3. Step 3: The bar chartA bar chart uses bars of equal width, whose length or height shows the quantity of each category; one bar per category, and a longer bar means more. In the subject survey, the English bar is tallest (12) and the Chinese bar shortest (8), and the gap is seen at a glance. Why is it good for comparison? Human eyes are very sensitive to length differences, and side-by-side bars make comparison direct and accurate. A common mistake is drawing bars of unequal width with no gaps, which readers confuse with a histogram; keep equal widths and leave gaps.
4. Step 4: The pie chartA pie chart divides a whole circle into sectors according to each category's percentage of the total, and all sectors together make 100%. Each sector's angle = 360° × its percentage. For example, if 10 of 40 students like Mathematics, the share is 25% and the sector angle = 360° × 25% = 90°. Why use angles? Sector area is proportional to its angle, so the angle directly reflects the part-to-whole relation. A common mistake is sector angles that do not sum to 360°; add up all the angles before drawing.
5. Step 5: The line graphA line graph joins data points with straight segments in order and is best for showing trends over time. For example, recording the daily temperature of a week as 20, 22, 25, 24, 27, 26, 28 degrees, the connected line makes rises and falls immediate; monthly sales similarly reveal peak and quiet seasons. Why join the points? The direction of the segments shows the direction of the trend, far more intuitive than a list of numbers. A common mistake is using a line graph for unrelated categories; categories have no order, and joining them misleads readers.
6. Step 6: Choosing the right chartChoose a chart by its purpose: comparing quantities across categories calls for a bar chart; showing parts of a whole calls for a pie chart; showing change over time calls for a line graph. For example, compare the popularity of four subjects with a bar chart, show Mathematics as a share of all choices with a pie chart, and display yearly sales movement with a line graph. Why not mix them? Each chart highlights one kind of information, and the wrong chart distorts the message. A common mistake is drawing a bar chart when the question asks for proportions; decide the nature of the data first.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Statistics = collect, organize, analyze, present data
• Frequency = how many times appears
• Bar chart: compare categories
• Pie chart: show proportion
• Line graph: show trend