Data Handling

1Summary 重點摘要

How to collect, organize and analyze data: survey, table, mean.

2Vocabulary cards Vocabulary

3Step by step Steps

1. 1. Ways of collecting dataStatistics begins with collecting data, commonly in three ways: a survey (asking people designed questions), observation (recording what actually happens, such as counting cars passing in a period) and experiment (measuring, such as recording every classmate's height). Questionnaire items must be clear with complete, non-overlapping options, and leading questions must be avoided — otherwise the data collected will not be reliable.
2. 2. Population and sampleThe population is the entire group under study; a sample is the part drawn from it. For example, all 1000 students of a school form the population, and 50 interviewed students form a sample. Sampling saves time and cost, but the sample must be large enough and randomly chosen in order to be representative — surveying only your own class is a biased sample, and conclusions drawn from it cannot be trusted.
3. 3. Frequency tablesA frequency table lists how often each category appears and is the basic tool for organising raw data. For a survey of favourite subjects: Chinese 8 students, English 12, Mathematics 10 — the numbers 8, 12 and 10 are the frequencies. Adding all frequencies should recover the total surveyed (30 students), which is a quick way to spot missing entries; the table is also the foundation for drawing bar charts later.
4. 4. MeanThe mean equals the sum of all values divided by how many there are. For scores 60, 70, 80, 90: the sum is 60 + 70 + 80 + 90 = 300 across 4 values, so the mean is 300 ÷ 4 = 75. Because the mean uses every value, it is easily dragged by extremes — adding one score of 0 pulls it down at once. After calculating, sanity-check that the result lies between the smallest and largest values.
5. 5. MedianThe median is the middle value once the data are arranged in order. For 60, 70, 80, 90, 100 the middle value is 80, so the median is 80. Two cautions: sorting may never be skipped, since taking the middle of unsorted data is always wrong; and with an even number of values the median is the average of the middle two — for 60, 70, 80, 90 it is (70 + 80) ÷ 2 = 75. The median resists extreme values, which suits data with large gaps.
6. 6. Mode and choosing among the threeThe mode is the value appearing most often. In 60, 70, 70, 80, 90 the value 70 appears twice and the rest once, so the mode is 70; a data set may have several modes, or none at all when every value appears once. Choosing among the three averages: use the mean for fairly even data, the median when extremes are present, and the mode is the only option for category data such as favourite colours. Exams often ask for all three from one data set, so keep the definitions apart.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Collect data: survey, observation, experiment
• Population vs sample
• Mean = sum ÷ count
• Median = middle after sorting
• Mode = appears most often