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What percentage of observation lie outside interquartile range of any distribution?

Mathematics
WAEC 1996

What percentage of observation lie outside interquartile range of any distribution?

  • A. 121/2%
  • B. 25%
  • C. 50%
  • D. 621/2 %
  • E. 75%
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Correct Answer: Option C
Explanation

Q1 represents the value below which 25% of the data falls, while Q3 indicates the value below which 75% of the data falls (or above which 25% falls). Consequently, the percentage of data outside the interval [Q1, Q3] is 50%, composed of 25% on each side.

This principle applies to any distribution, as quartiles are determined by order statistics and cumulative probabilities, independent of the distribution's shape


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