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IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis

For a sample of 11 policy sizes, the ordered values give a lower quartile of ₹4 lakh, a median of ₹7 lakh and an upper quartile of ₹12 lakh. The smallest observation is ₹1 lakh and the largest is ₹40 lakh. Using the rule that a point is an outlier if it lies above Q3 + 1.5×IQR, which statement about the boxplot is correct?

The upper fence is ₹24 lakh and the maximum of ₹40 lakh is plotted as an outlier. The IQR is 8, so the fence is 12 + 1.5×8 = 24, and ₹40 lakh exceeds it.

  1. AThe upper fence is ₹18 lakh and the maximum is plotted as an outlier
  2. BThe upper fence is ₹24 lakh and the maximum is plotted as an outlierCorrect
  3. CThe upper fence is ₹20 lakh and the maximum lies within the whisker
  4. DThe upper fence is ₹24 lakh and the whisker extends to ₹40 lakh
  5. The upper fence is ₹36 lakh and the maximum is plotted as an outlier

Explanation

IQR = 12 − 4 = 8. Upper fence = 12 + 1.5×8 = 24. Since 40 > 24, the maximum is an outlier and is plotted separately. Using Q3 + 1.5×IQR with IQR mistaken as 4 would give 18.

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