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.
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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 — Identifying Skewness from Frequency
A store collected weekly sales data of 50 branches. Most branches sold around 1,000–1,200 units, but 3 branches sold over 5,000 units.
What type of skewness would the frequency distribution show?
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Right-skewed (positively skewed) distribution 正偏态分布📝 点击解析
大多数数据集中在低值区，少数极大值拉长右尾 → 正偏态。Question 3 — Relative Frequency Interpretation
In a survey of 200 hotel guests: Poor=10, Fair=30, Good=120, Excellent=40.
If a new guest is randomly chosen, what is the probability that the guest rated at least “Good”?
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(120+40)/200 = 160/200 = 0.8 (80%)📝 点击解析
至少为 Good 包括 Good 和 Excellent。相对频率总和=0.8。Question 4 — Cumulative Frequency Application
A frequency distribution for delivery times (minutes):
0–10: 15 orders, 11–20: 25 orders, 21–30: 35 orders, 31–40: 20 orders, 41–50: 5 orders.
Find the cumulative percentage for ≤30 minutes.
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(15+25+35) / 100 = 75%📝 点击解析
≤30 min = 前三组的总和=75/100=75%。Question 5 — Choosing the Chart
A manager wants to compare yearly growth of product sales (continuous data) for three products. Should they use a bar chart, pie chart, or line chart?
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Line chart 折线图📝 点击解析
连续数值型数据（时间序列）趋势最好用折线图，条形图/饼图只适合分类数据比例。Question 6 — Pareto Chart Priority
A call center records complaints: Billing=300, Network=500, App=100, Other=100.
If management can only fix two issues, which should they prioritize?
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Network and Billing (total 800/1000 = 80%) 网络问题和账单问题📝 点击解析
Pareto 80/20 原则 → 最大的两个问题解决后覆盖 80% 投诉。Question 7 — Pie Chart Angle
A company’s market share: A=20%, B=30%, C=50%.
What is the angle for B in a pie chart?
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108°📝 点击解析
30% × 360° = 108°。Question 8 — Misleading Chart Design
Explain why using a 3D pie chart for 10 categories of small market shares can mislead decision-making.
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It distorts slice sizes, making small categories hard to compare. 3D 饼图会扭曲面积，使小份额更难比较。📝 点击解析
3D 效果改变视觉感受 + 类别太多 → 解读困难，误导管理层。Question 9 — Constructing a Pivot Table
From raw data of 200 survey responses (Excellent/Good/Fair/Poor), describe the process to use Excel Pivot Table to construct a frequency distribution.
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Insert Pivot Table → Drag Rating to Row Labels → Drag Rating to Values (Count). 插入数据透视表 → 拖动“评分”到行标签 → 再拖动“评分”到数值区（计数）。📝 点击解析
数据透视表通过 COUNT 快速汇总频数，避免逐个 COUNTIF。Question 10 — Comparing Frequencies
Two stores collect customer ratings:
Store A: Poor=10, Fair=20, Good=50, Excellent=20 (n=100)
Store B: Poor=15, Fair=30, Good=45, Excellent=10 (n=100)
Which store has higher relative satisfaction (Good+Excellent)?
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Store A = 70% vs Store B = 55% → Store A higher📝 点击解析
A: (50+20)/100=70%。B: (45+10)/100=55%。满意度 A > B。Question 11 — Interpreting Cumulative Graph
In a cumulative percentage graph, 80% of students scored ≤75 points.
Interpret this in plain language.
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80% of students had scores of 75 or lower. 80% 学生成绩不超过 75 分。📝 点击解析
累积百分比图的纵坐标直接表示“至某值以下的人群比例”。Question 12 — Business Application of Pareto
A supermarket identifies 100 different complaints but finds that 5 types account for 85% of total.
How should management apply Pareto analysis here?
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Focus on fixing the 5 main complaint types first. 优先解决前 5 类投诉问题。📝 点击解析
80/20 法则 → 少数关键问题贡献大部分结果。处理 5 大投诉可显著改善整体满意度。Question 13 — Choosing Between Bar and Pie Chart
When showing proportions of age groups in a population (10–19, 20–29, 30–39…), which chart is better: bar chart or pie chart? Why?
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Bar chart, because it allows better comparison across many categories. 条形图，因为类别多时比较更清晰。📝 点击解析
饼图适合少类别。年龄分组多时，条形图便于精确比较。Question 14 — Detecting Data Errors
If the relative frequencies in a distribution sum to 1.12, what mistake was likely made?
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Double-counting or misclassification of data. 重复计数或分类错误。📝 点击解析
相对频率必须=1。>1 表明数据有重叠或输入错误。Question 15 — Market Share Analysis
A market has 4 firms with shares: 40%, 25%, 20%, 15%.
If two smallest firms merge, what is their new rank and pie chart share?
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New firm = 35%, ranked 2nd largest.📝 点击解析
20%+15%=35%。比 40% 小，但比 25% 大 → 第二。饼图切片=35%。Question 16 — Outlier Impact
How would one “Excellent” rating among 1,000 “Poor” ratings affect a pie chart?
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It would be visually negligible (≈0.1%) and not noticeable. 几乎不可见 (≈0.1%)。📝 点击解析
比例极小，切片太薄，饼图无法清晰传达。Question 17 — Red Lobster Example
In Red Lobster data, “Overpriced”=789, total=1,722.
Compute its percent frequency and interpret it.
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45.8% → Nearly half of complaints were about overpriced food. 45.8% → 投诉中近一半是“价格过高”。📝 点击解析
789 ÷ 1722 ≈ 0.458。解释时要转化为实际业务含义。Question 18 — Ranking with Cumulative Percent
In complaint data: Issue A=40%, B=30%, C=20%, D=10%.
At which point (after which issue) does cumulative percent exceed 70%?
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After Issue B (40%+30%=70%).📝 点击解析
累计加和：A=40%，B=70%。B 后累计已达 70%。Question 19 — Managerial Decision from Data
A bar chart shows customer dissatisfaction reasons, with “Service” bar twice as tall as “Price” bar.
How should management allocate improvement resources?
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Prioritize service improvement, since it accounts for double the complaints. 优先改进服务，因为其投诉量是价格的两倍。📝 点击解析
条形图直接比较频数 → 高柱形=高优先级问题。Question 20 — Misinterpretation of Percentages
A report says “70% of complaints are about food taste, 40% about service.”
What is the problem with this statement?