The data are \(10,12,14,14,18,19,21,25,p,q\), where \(p,q\) are consecutive positive integers and \(p<q\). The unique mode is 14 and the median is 15.5. Find \(p,q\).
Fifteen scores were reported with mean 10.4, but scores 13 and 17 should have been omitted. Find the correct mean of the remaining 13 scores.
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