Question 1 — Advanced: International Expansion Decision
A retail company compares customer spending (USD) between its U.S. stores and new Asian stores.
- U.S.: Mean = 120, SD = 25, CV = 20%, Skewness = +0.2
- Asia: Mean = 95, SD = 35, CV = 37%, Skewness = +1.1
Management wants to decide which market shows more stable and predictable spending patterns, even if average is lower.
📖 点击查看答案
The Asian market has higher variability (CV=37% vs. 20%) and stronger right-skew (1.1 vs. 0.2).
→ U.S. market is more predictable despite a higher mean.
📝 点击查看解析
- CV 允许跨均值比较相对波动，亚洲市场风险更大。 - 正偏态意味着部分顾客大额消费，但大部分顾客集中在较低区间 → 可预测性差。 - 若公司目标是“稳定预测”，美国市场更优。Question 2 — Advanced: Evaluating Employee Productivity
Two departments are compared on average weekly tasks completed per employee:
- Dept A: Mean = 52, Median = 50, Range = 25, IQR = 10
- Dept B: Mean = 50, Median = 41, Range = 60, IQR = 35
The HR director wants to reward the department with higher consistency in workforce performance.
📖 点击查看答案
Dept A shows higher consistency (narrower IQR=10 vs. 35, smaller range).
📝 点击查看解析
- Dept A: Mean≈Median → 分布对称，波动小。 - Dept B: Mean > Median → 右偏，极差和 IQR 较大，说明员工之间差异大。 - 奖励目标是稳定性 → 选择 A。Question 3 — Advanced: Selecting a Supplier Based on Delivery Times
Supplier delivery times (hours) for 30 shipments:
- Supplier X: Mean = 5.2, SD = 0.9, CV = 17%
- Supplier Y: Mean = 4.8, SD = 1.7, CV = 35%, Kurtosis = 2.8
If the company values on-time reliability more than slightly shorter mean times, which supplier should they choose?
📖 点击查看答案
Supplier X. Smaller SD and CV → more consistent.
Supplier Y has slightly faster mean but high variability and fat tails (Kurtosis=2.8).
📝 点击查看解析
- Supplier Y’s high kurtosis means occasional extreme delays. - Supplier X’s higher mean (0.4 hours slower) is offset by greater reliability. - 稳定性优先 → Supplier X 更合适。Question 4 — Advanced: Investment Risk Evaluation
Two mutual funds report annual returns:
- Fund A: Mean = 8%, SD = 5%, CV = 62.5%, Skewness = –0.5
- Fund B: Mean = 10%, SD = 9%, CV = 90%, Skewness = +0.8
If an investor is risk-averse and dislikes both volatility and downside risk, which fund is preferable?
📖 点击查看答案
Fund A, despite lower mean return, offers lower volatility and negative skew is mild compared to Fund B’s high CV.
📝 点击查看解析
- CV highlights Fund B’s risk: 90% 波动远高于 A 的 62.5%。 - Skewness: A 略微左偏，风险在于偶尔低收益；B 右偏，均值可能被少数高收益拉高，不利于稳健投资。 - 风险厌恶投资者倾向于选 A。Question 5 — Advanced: Deciding Training Effectiveness
Two training programs were piloted: test scores (out of 100) from participants:
- Program Alpha: Mean = 78, SD = 4, Kurtosis = –0.5
- Program Beta: Mean = 79, SD = 10, Kurtosis = +3.5
If the company values both high performance and consistency, which program should be scaled?
📖 点击查看答案
Program Alpha: slightly lower mean but much smaller SD, flatter distribution → consistent improvement.
📝 点击查看解析
- Beta has marginally higher mean but heavy tails (kurtosis=3.5) → 部分学员高分，部分低分 → 不稳定。 - Alpha 稳定性更强，更可预测。 - 综合考虑 → Alpha 更值得推广。Question 6 — Advanced: Customer Satisfaction Ratings
Two service centers collected satisfaction scores (1–10):
- Center A: Mean = 8.1, SD = 1.8, Skewness = –0.6
- Center B: Mean = 8.3, SD = 2.5, Skewness = +1.2
If management wants to highlight the center that delivers a uniformly good experience, which should they showcase?
📖 点击查看答案
Center A: slightly lower mean but less spread and mild negative skew → more consistent experience.
📝 点击查看解析
- B 的平均分更高，但波动大且右偏 → 部分用户打低分。 - A 分布集中，负偏意味着大多数顾客满意，少数打低分。Question 7 — Advanced: Inventory Turnover Days
Two warehouses record turnover days:
- Warehouse X: Median = 15, IQR = 4, Range = 18
- Warehouse Y: Median = 16, IQR = 2, Range = 25
Which warehouse shows tighter control over turnover performance?
📖 点击查看答案
Warehouse Y: smaller IQR (2 vs. 4) → middle 50% more consistent, even though extreme range is larger.
📝 点击查看解析
- 极差受极端值影响，不适合作稳定性评价。 - IQR 衡量中间 50% 稳定度，Y 更佳。Question 8 — Advanced: Supplier Quality Scores
Quality defect rates (per 1,000 items):
- Supplier M: Mean = 7.0, SD = 3.2, CV = 45%
- Supplier N: Mean = 6.8, SD = 1.0, CV = 15%
Which supplier offers more reliable quality?
📖 点击查看答案
Supplier N: slightly lower mean and much smaller CV → defects are more predictable.
📝 点击查看解析
- CV 可跨均值比较。 - N 的相对波动性远低于 M → 品质更稳定。Question 9 — Advanced: Loan Approval Times
Two banks report approval times (days):
- Bank A: Mean = 12, SD = 2, Kurtosis = –0.7
- Bank B: Mean = 11, SD = 3, Kurtosis = +2.5
For a fintech app recommending “fast and predictable” partners, which bank should be recommended?
📖 点击查看答案
Bank A: slightly slower mean but smaller SD and flatter tails → fewer extreme delays.
📝 点击查看解析
- B 虽快一天，但尾部肥厚 (kurtosis=2.5) → 部分客户等待过长。 - A 更可预测，适合推荐。Question 10 — Advanced: Online Course Completion Rates
Two e-learning platforms report student completion rates (%):
- Platform A: Mean = 72, Median = 70, Range = 50, IQR = 20
- Platform B: Mean = 74, Median = 65, Range = 60, IQR = 35
Which platform demonstrates more equitable learning outcomes?
📖 点击查看答案
Platform A: narrower IQR → more consistent outcomes across learners.
📝 点击查看解析
- A 的均值略低但中位数接近均值 → 分布对称。 - B 均值被部分高完成率拉高，IQR 大，学习结果差距大。Question 11 — Advanced: Production Line Cycle Times
Cycle times (minutes):
- Line 1: Mean = 42, SD = 3, CV = 7%, Skewness = +0.3
- Line 2: Mean = 41, SD = 5, CV = 12%, Skewness = +1.0
If the goal is stable throughput, which line should be expanded?
📖 点击查看答案
Line 1: slightly slower mean but lower CV and near-symmetric distribution.
📝 点击查看解析
- 产能规划看一致性 → CV 是核心指标。 - Line 1 更稳定。Question 12 — Advanced: Customer Purchase Frequency
Two membership tiers:
- Silver: Mean purchases/year = 10, SD = 6, Skewness = +2.0
- Gold: Mean purchases/year = 14, SD = 4, Skewness = +0.4
Which group is more predictable for forecasting demand?
📖 点击查看答案
Gold members: higher mean and smaller skew → demand more consistent.
📝 点击查看解析
- Silver 平均较低，右偏严重，说明少数客户购买频繁。 - Gold 波动小，分布更对称。Question 13 — Advanced: Delivery Fee Comparison
Delivery fee data (RMB):
- Company A: Median = 25, IQR = 4, Range = 20
- Company B: Median = 27, IQR = 2, Range = 30
Which company provides more consistent fee levels to customers?
📖 点击查看答案
Company B: narrower IQR despite larger range.
📝 点击查看解析
- Range 被极端值拉大，不适合稳定性比较。 - B 的中间费用更集中。Question 14 — Advanced: Marketing Campaign ROI
Two campaigns report ROI:
- Campaign X: Mean = 1.25, SD = 0.20, CV = 16%
- Campaign Y: Mean = 1.30, SD = 0.50, CV = 38%
If management must choose one for scaling, which is safer?
📖 点击查看答案
Campaign X: lower ROI mean but much more stable CV.
📝 点击查看解析
- 投资决策要兼顾收益与风险。 - Y 虽然均值高，但波动过大，结果不可预测。Question 15 — Advanced: Website Load Times
Websites record load times (seconds):
- Site A: Mean = 2.8, SD = 0.6, Kurtosis = +3.0
- Site B: Mean = 3.0, SD = 0.4, Kurtosis = –0.5
Which site delivers a better user experience?
📖 点击查看答案
Site B: slightly slower mean but flatter distribution and fewer extreme slow loads.
📝 点击查看解析
- A 的平均快，但峰度高 → 偶尔极慢影响用户感知。 - B 更稳定，整体体验更好。Question 16 — Advanced: Employee Overtime Hours
Average monthly overtime hours:
- Team A: Mean = 12, Median = 12, Range = 20, IQR = 6
- Team B: Mean = 14, Median = 11, Range = 30, IQR = 12
Which team faces greater workload inequality?
📖 点击查看答案
Team B: wider IQR and mean > median (right-skew).
📝 点击查看解析
- A 均值≈中位数 → 分布对称。 - B 均值大于中位数，且离散度更高，说明部分人加班远超其他人。Question 17 — Advanced: Customer Waiting Times
Waiting time (minutes):
- Branch A: Mean = 8.0, SD = 2.5, Skewness = +1.5
- Branch B: Mean = 8.5, SD = 1.8, Skewness = +0.3
Which branch is better aligned with service quality goals?
📖 点击查看答案
Branch B: slightly higher mean but more stable, nearly symmetric distribution.
📝 点击查看解析
- 服务质量关键在于减少极端长等待。 - A 的正偏态说明部分顾客等待过久。Question 18 — Advanced: Manufacturing Yield Rates
Yield rates (%):
- Plant X: Mean = 93, SD = 4, CV = 4.3%
- Plant Y: Mean = 95, SD = 7, CV = 7.4%
Which plant is more suitable for critical contracts requiring stable quality?
📖 点击查看答案
Plant X: slightly lower mean but much smaller CV.
📝 点击查看解析
- 高风险合同更重视稳定性而非均值极致。 - X 的相对波动小，更可靠。Question 19 — Advanced: Housing Price Analysis
Neighborhoods:
- Area A: Median = 420k, IQR = 30k, Skewness = +0.2
- Area B: Median = 400k, IQR = 80k, Skewness = +1.5
Which area is more attractive for buyers seeking price predictability?
📖 点击查看答案
Area A: narrower IQR, near-symmetric distribution.
📝 点击查看解析
- B 价格分布更分散，右偏严重 → 房价差距大。 - A 价格更集中，预测性高。Question 20 — Advanced: Airline Flight Delays
Two airlines report delays (minutes):
- Airline 1: Mean = 18, SD = 9, CV = 50%, Kurtosis = +2.9
- Airline 2: Mean = 20, SD = 6, CV = 30%, Kurtosis = –0.2
Which airline should a business traveler choose?
📖 点击查看答案
Airline 2: slightly longer mean delay but much lower variability and fewer extreme delays.