Discussion
The \(90^{m}\) sample percentile of 80 observations is 6. Suppose 6 is added to the 7 largest observations and 3 is subtracted from the remaining observations. The \(90^{m}\) sample percentile of the modified 80 observations is :
Answer: B
The new 90th percentile is 3.
For 80 observations the 90th percentile sits at rank \(0.9 \times 80 = 72\), between the 72nd and 73rd smallest values. The 7 largest observations occupy ranks 74 to 80, so the percentile is determined by observations among the remaining 73.
Subtracting 3 from those 73 shifts them all down by 3 without changing their order, and adding 6 to the top 7 keeps those above them. So the ranks are unchanged and the percentile moves from 6 to
\[ 6 - 3 = 3 \]
12 would follow if the percentile point were among the 7 largest and the change were added, and 9 adds 3 instead of subtracting it.
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