Question 1 — Designing a Frequency Distribution
A university surveyed 120 students on weekly hours spent on part-time jobs. The data ranges from 0 to 30 hours.
Design a frequency distribution table with 6 equal-width classes.
📖 点击查看答案
Class width = (30-0)/6 = 5 Classes: 0–4, 5–9, 10–14, 15–19, 20–24, 25–30📝 点击解析
频数分布的关键是选择区间宽度。范围=30，分6组 → 每组宽度=5。 区间为 [0–4], [5–9], [10–14], [15–19], [20–24], [25–30]。Question 2 — Choosing Number of Classes
A dataset of 5,000 sales records needs to be grouped into a frequency distribution.
Would you recommend 5, 10, or 20 classes? Why?
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20 classes.📝 点击解析
数据量大时应选择更多组数以避免信息丢失。5000条数据若只分5组会过于粗糙，10组仍显不足。20组能更好展示分布细节。Question 3 — Detecting Skewness
A histogram of monthly incomes shows most employees earn between 5k–8k RMB, with a long right tail up to 50k RMB.
What kind of skewness does this distribution show?
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Right-skewed (positively skewed).📝 点击解析
大多数数值集中在低区间，而高值少数但拉长尾巴 → 典型的正偏态。Question 4 — Comparing Two Groups
Two classes recorded GPA distributions:
- Class A: GPAs mostly between 3.0–3.5.
- Class B: GPAs spread evenly between 2.0–4.0.
Which class shows greater variability, and why?
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Class B shows greater variability.📝 点击解析
Class A数据集中，说明离散程度小；Class B均匀分布在更宽区间，说明变异性更大。Question 5 — Choosing Class Width
A manager records repair costs ranging from 120 RMB to 520 RMB.
If she wants 8 classes, what class width should she use?
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Width = (520–120)/8 = 50 RMB📝 点击解析
范围=400，分8组 → 组宽=50。每组如120–169, 170–219… 直到520。Question 6 — Misleading Frequency Table
If a frequency table uses unequal class widths, why might this be misleading? Give one scenario.
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Unequal widths distort comparisons; e.g., comparing sales in a 0–100 interval vs. 101–110 interval exaggerates smaller group frequencies.📝 点击解析
不等组宽会导致比例失真。例：一组宽100，另一组仅10，但用频数直接比较，会误导读者。Question 7 — Cumulative Frequency Interpretation
In a GPA distribution, cumulative % below 3.0 = 40%.
What does this mean in plain language?
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40% of students have GPA less than 3.0.📝 点击解析
累积频率是“到某点为止”的比例。小于3.0的GPA学生占40%。Question 8 — Business Application
A retailer uses frequency distribution of daily sales to set staffing levels.
How can this information be applied?
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By identifying peak sales ranges, the retailer can allocate more staff on busy days.📝 点击解析
频率分布显示高销量日的集中区间 → 企业可据此调整人力配置，避免排队和顾客流失。Question 9 — Comparing Frequency Tables
Two stores show:
- Store A: Most sales in 100–200 RMB range.
- Store B: Sales evenly spread across 50–500 RMB.
Which store has more consistent customer spending?
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Store A has more consistent spending.📝 点击解析
Store A顾客支出集中；Store B分布较分散，说明消费不稳定。Question 10 — Designing a Histogram
Why is it inappropriate to create a histogram for categorical data?
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Histograms require numerical intervals; categorical data lacks inherent order and equal spacing.📝 点击解析
直方图依赖区间和数轴；分类数据（如性别、颜色）无连续性和等距概念，应使用条形图。Question 11 — Ogive Usage
A company plots an ogive of delivery times.
How could this be used to guarantee service-level targets?
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By reading cumulative % at specific time thresholds (e.g., 95% deliveries < 3 days).📝 点击解析
累积曲线可直接读出“多少比例在某时限内完成”。这可用于KPI设定，如保证95%在3天内送达。Question 12 — Impact of Grouping
How does grouping continuous data into classes affect detail? Provide one advantage and one disadvantage.
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Advantage: Simplifies analysis. Disadvantage: Loses exact data points.📝 点击解析
优点：数据简化，趋势清晰。缺点：具体值被隐藏，精度下降。Question 13 — Business Risk Example
Insurance claims are grouped into frequency classes.
How might cumulative frequency help risk managers?
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It shows % of claims below a threshold, useful for setting premiums or reserves.📝 点击解析
累积频率揭示“多少索赔额低于某值”。保险公司可据此决定定价与准备金。Question 14 — Wrong Grouping
A dataset ranges 52–109. Someone uses 5 classes width=15.
What’s wrong with this choice?
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Width doesn’t cover entire range evenly → last class ends at 127, leaving gaps/empty intervals.📝 点击解析
范围=57。用组宽15会超过范围，产生不必要的空区间。应选更合适宽度(≈10)。Question 15 — Detecting Outliers
A frequency table of exam scores shows most students between 60–90, but 2 students scored 10 and 100.
How should this be treated?
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Recognize them as outliers; consider reporting separately or adjusting class intervals.📝 点击解析
极端值会扭曲频率分布。应单独标记或在分析中说明，而非简单纳入常规组。Question 16 — Comparing Cumulative Curves
Two products’ cumulative sales curves are plotted.
Product A reaches 80% sales by mid-year; Product B only 40%.
Which has faster early sales growth?
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Product A has faster early sales growth.📝 点击解析
累积曲线陡峭表示增长快。Product A半年内完成80%销量，远超Product B。Question 17 — Cross-Analysis
A university collects GPA data by gender.
What kind of table/graph should be used to compare frequency distributions between groups?
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A side-by-side histogram or grouped frequency table.📝 点击解析
分组直方图/频率表能直观对比男女生分布差异。Question 18 — Pareto Principle
A store finds 20% of products account for 80% of sales.
Which chart best shows this?
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Pareto chart.📝 点击解析
帕累托图结合条形和累积线，最能体现“二八法则”。Question 19 — Business Forecast
A bank groups loan defaults by age bracket.
How might this frequency distribution inform future lending policies?
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By identifying high-default age groups, the bank can adjust credit policies or require stricter checks.📝 点击解析
频率分布揭示违约集中群体 → 银行可相应提高利率或审查门槛。Question 20 — Combining Categorical & Quantitative Data
A survey collects both customer age (quantitative) and preferred brand (categorical).
How should data be analyzed?