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For the frequency distribution below, what is the position of the upper quartile? Item size: 1, 2, 3, 4, 5, 6, 7 Frequencies: 2, 4, 5, 8, 7, 3, 2

1. the \((31+1)/4\)th observation
2. the \(2((31+1)/4)\)th observation
3. the \(3((31+1)/4)\)th observation
4. the \(4((31+1)/4)\)th observation

Correct answer: the \(2((31+1)/4)\)th observation

Solution

The upper quartile, or the 75th percentile, is found by calculating the position using the formula for the quartile, which in this case is represented as the 2nd quartile position, hence the correct option is the 2((31+1)/4)th observation.

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