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 跨均值比较波动，亚洲市场相对波动率更大。 - 偏度 +1.1 → 分布右偏严重，极少数大额消费拉升均值。 - 美国市场更对称且波动小，更具可预测性。Question 2 — Advanced: Salary Inequality Audit
Two companies report employee salaries (in $1,000):
- Firm A: Mean = 75, Median = 72, Q3 = 80
- Firm B: Mean = 75, Median = 55, Q3 = 140
Which firm shows greater income inequality, and why?
📖 点击查看答案
Firm B.
→ The large mean–median gap and wide Q3 indicate more inequality.
📝 点击查看解析
- Firm A → 均值≈中位数，分布平稳。 - Firm B → 中位数远低于均值，说明高收入拉升均值。 - Q3=140 显示高端差距更大。Question 3 — Advanced: Airline Delay Risk
Two airlines’ delay times (minutes):
- Airline X: Mean=18, SD=6, Skew=+0.1
- Airline Y: Mean=16, SD=15, Skew=+2.5
Which is more reliable for business travelers?
📖 点击查看答案
Airline X.
📝 点击查看解析
- X 延误略高，但波动小，分布对称。 - Y 延误平均更低，但波动大且右偏严重 → 存在极端延误。Question 4 — Advanced: Housing Affordability Policy
City rents: Mean = $1,800, Median = $1,300, 80th percentile = $3,000.
Gov’t wants to subsidize bottom 60% renters.
📖 点击查看答案
Use 60th percentile (~$1,600).
📝 点击解析
- 均值受极端高租金扭曲。 - 政策目标应直接采用第60百分位。Question 5 — Advanced: Executive Pay Outlier
CEO salaries (M USD): [1.2, 1.5, 1.6, 1.8, 2.0, 2.1, 15.0].
📖 点击查看答案
15.0 is an outlier; median better reflects pay.
📝 点击解析
- Q1=1.5, Q3=2.05, IQR=0.55 → 上界=2.875。 - 15.0 >> 2.875 → 异常值。 - 均值被拉高，中位数更合理。Question 6 — Advanced: Global Test Score Comparison
PISA scores:
- Country A: Mean=510, SD=20
- Country B: Mean=495, SD=10
📖 点击查看答案
Country B (more consistent).
📝 点击解析
- 虽然A均值高，但B波动更小。 - 若重视稳定，B更优。Question 7 — Advanced: Hospital Wait Times
Wait times (min): Mean=45, Median=30, Mode=20, Skew=+2.0.
📖 点击查看答案
Right-skewed; Median=30 best describes typical wait.
📝 点击解析
- 均值被极端值拉高。 - 众数太低，不代表平均体验。 - 中位数=30 更贴近大多数病人。Question 8 — Advanced: Retail Inventory Risk
Monthly sales:
- Category A: Mean=800, CV=10%
- Category B: Mean=500, CV=40%
📖 点击查看答案
Category A is safer.
📝 点击解析
- CV比较：A=10%，B=40%。 - A需求更稳定 → 库存风险更低。Question 9 — Advanced: Education Policy Funding
Scores (0–100): Mean=68, Median=72, Q1=60, Q3=75.
Gov’t funds bottom quartile schools.
📖 点击查看答案
Cutoff = Q1=60.
📝 点击解析
- Q1=60 表示最低25% ≤60。 - 政策门槛应设在Q1。Question 10 — Advanced: Premium Client Marketing
Credit spending: Median=$450, 90th percentile=$1,200.
📖 点击查看答案
Mass: target $450; Premium: >$1,200.
📝 点击解析
- 中位数用于普遍客户定位。 - 90th 百分位揭示高端群体 → 定制化服务。Question 11 — Advanced: Country Risk in Investments
Two countries’ GDP growth rates (%):
- Country A: Mean=3.5, SD=1.0, Skew=–0.3
- Country B: Mean=3.5, SD=2.8, Skew=+1.5
📖 点击查看答案
Country A is less risky.
📝 点击解析
- 均值相同，但A波动小，负偏度 → 下行风险有限。 - B波动大且右偏 → 不确定性高。Question 12 — Advanced: Choosing KPI for Call Center
Response times (sec) show many extreme delays.
📖 点击查看答案
Median response time.
📝 点击解析
- 均值受异常延迟拖高。 - 中位数更代表大多数客户体验。Question 13 — Advanced: Product Pricing Strategy
A hotel’s prices: Mode=$120, Median=$150, Mean=$180.
📖 点击查看答案
Median = $150 should be standard advertised price.
📝 点击解析
- 分布右偏，均值受高价房拉高。 - 众数=120过低，不能反映整体定位。 - 中位数=150 平衡合理。Question 14 — Advanced: Detecting Fake Data
A dataset of student grades shows Mean=75, Median=75, SD=0.
📖 点击查看答案
Data likely fake/unrealistic (all values identical).
📝 点击解析
- 标准差=0 表示无差异，所有分数相同。 - 不符合真实分布，可能是伪造数据。Question 15 — Advanced: Comparing Retail Chains
Chain A sales: Mean=200, CV=5%.
Chain B sales: Mean=400, CV=25%.
Which is more predictable for franchise investment?
📖 点击查看答案
Chain A.
📝 点击解析
- A均值较低，但相对稳定。 - 投资角度更重视风险控制 → A更优。Question 16 — Advanced: Detecting Market Skew
Housing data: Mean=$400k, Median=$300k, Mode=$250k.
📖 点击查看答案
Right-skewed distribution; few luxury homes pull mean upward.
📝 点击解析
- 均值>中位数>众数 → 明显右偏。 - 高端房产价格扭曲均值。Question 17 — Advanced: School Ranking
School A: Mean=85, SD=12.
School B: Mean=83, SD=5.
Which school provides more consistent outcomes?
📖 点击查看答案
School B.
📝 点击解析
- A 均值更高，但波动性更大。 - B 稳定性更好，适合追求一致性的政策或家长选择。Question 18 — Advanced: Trimmed Mean in Judging
Diving scores: [9.5, 9.6, 9.7, 9.5, 9.8, 2.0, 9.6, 9.7].
📖 点击查看答案
5% trimmed mean ≈ 9.63 (after removing 2.0 and 9.8).
📝 点击解析
- 极端低分 (2.0) 和高分 (9.8) 去掉后 → 平均约 9.63。 - 更公平反映裁判多数意见。Question 19 — Advanced: Income Policy
National incomes: Q1=20k, Median=40k, Q3=70k.
Gov’t considers raising taxes on “top quartile.”
📖 点击查看答案
Apply tax for incomes ≥70k.
📝 点击解析
- Q3=70k → 顶部25% ≥70k。 - 设此为政策门槛符合四分位定义。Question 20 — Advanced: Product Demand Volatility
Two tech products’ monthly sales:
- Product X: Mean=10,000, SD=500
- Product Y: Mean=10,000, SD=2,500
Which product line is riskier for forecasting?
📖 点击查看答案
Product Y (higher SD).