Collecting data
Introduced| English | Meaning |
|---|---|
| population/ˌpɒpjʊˈleɪʃn/ | The entire set of individuals, items or outcomes about which a statistical study seeks information. |
| sample/ˈsæmpl/ | A subset of a population selected for observation, measurement or analysis. |
| representative/ˌreprɪˈzentətɪv/ | Reflecting the relevant characteristics of the larger group or population. |
| qualitative data/ˈkwɒlɪteɪtɪv ˈdeɪtə/ | qualitative data |
| quantitative data/ˈkwɒntɪteɪtɪv ˈdeɪtə/ | Data describing numerical amounts or measurements, rather than categories alone. |
| discrete/dɪˈskriːt/ | Consisting of separate, distinct values rather than a continuous range. |
| continuous/kənˈtɪnjuːəs/ | Changing without a break or jump, or taking every value within an interval. |
| histogram/ˈhɪstəɡræm/ | A graph of grouped numerical data using adjoining bars whose areas represent frequencies. |
Define whom a finding describes
- A population 总体 is the target group; a sample 样本 is the observed subset. A class survey can describe that class without establishing a school-wide percentage.
- A suitably representative 有代表性的 sample requires attention to selection, participation and the question asked. A large voluntary response does not automatically resolve nonresponse.
Distinguish labels from measured amounts
- Qualitative data 定性数据 are categories. Quantitative data 定量数据 measure amounts; discrete 离散 data use distinct countable values, while continuous 连续 data are modelled over intervals.
- A numerical route label is still a category. Recorded continuous measurements can be rounded, so printed decimal precision alone does not decide the underlying type.
Match each variable to its data type.
Difficulty 2/5 · 140 coins + a small bonus on first completion today
Counted values are discrete; measured values are continuous. The type decides which chart is legitimate.
Match the display to the data
- A histogram 直方图 uses numeric class intervals. For unequal widths, frequency density is frequency divided by width so bar area represents frequency.
- Separate category bars and label units, scale and count scope. A pie chart requires mutually exclusive parts of a defined whole; missing responses must not silently become a known category.
Which chart suits continuous data such as height?
Difficulty 1/5 · 100 coins + a small bonus on first completion today
A histogram displays frequencies over numeric intervals. With unequal interval widths, use frequency density so area represents frequency; an empty interval can have zero height.
Two sampling plans have different risks. Asking a canteen queue excludes nonusers. Selecting every tenth name can cover the full roll, but needs a random start and a check for patterns in the ordering. Neither method guarantees honest responses or removes all nonresponse; record the actual procedure and limits.
To study canteen preferences across a school, which listed selection plan best covers the full student population?
Difficulty 1/5 · 100 coins + a small bonus on first completion today
Selection from the full roll can include nonusers. A systematic every-tenth-name plan needs a random start and a check for patterns; nonresponse remains a limitation, so it does not guarantee perfect representativeness.
State the denominator. If 60 of 200 students reply and 45 prefer later meetings, response rate is 30% and respondent preference is 75%. Preferences of the remaining 140 are unknown. Sheet 2.5 separates preference evidence from attendance evidence.
A larger sample removes bias caused by how the sample was chosen.
Difficulty 1/5 · 100 coins + a small bonus on first completion today
Increasing sample size alone does not remove systematic selection or nonresponse bias. Examine and improve the collection method and disclose remaining limits.
A truncated category-bar axis changes the visible comparison of heights. Use a zero baseline for straightforward magnitude comparisons, and make any exceptional scale choice explicit. A larger sample does not by itself fix a systematically selected sample.
A bar chart's vertical axis starts at 40 rather than 0. What must you do?
Difficulty 1/5 · 100 coins + a small bonus on first completion today
A truncated category-bar scale can exaggerate relative heights. A zero baseline supports magnitude comparisons; any exception needs a clear, justified scale rather than an unstated change.