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CMA Intermediate · Financial Management and Business Data Analytics · Introduction to Data Science for Business Decision-making

Monthly sales (₹ lakh) of a product are: 40, 42, 44, 46, 48, 50, 52, 54, 56, 100. Using Q1 = 44 and Q3 = 54 and the rule that outliers lie beyond 1.5 × IQR from the quartiles, which value(s) are outliers?

Only 100 is an outlier. The interquartile range is 10, so 1.5 times IQR is 15. The upper fence is 54 plus 15, which is 69, and the lower fence is 29. Only 100 lies outside these limits.

  1. AOnly 100, since the upper fence is 69Correct
  2. BBoth 40 and 100
  3. COnly 100, since the upper fence is 79
  4. DNo outliers, since the upper fence is 84

Explanation

IQR = 54 − 44 = 10; 1.5 × IQR = 15. Upper fence = 54 + 15 = 69; lower fence = 44 − 15 = 29. Only 100 exceeds 69 and 40 is above 29. Using 79 or 84 would come from wrongly multiplying IQR by 2.5 or 3.

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