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On the other hand, to compute the 42nd percentile using the definitionĀ 1.3.6 for the President inauguration data presented earlierĀ 1.3.2 consider s = 0.42. Since there are 6 numbers in our data set, then
\begin{equation*} (n-1)s + 1 = 5 \cdot 0.42 + 1 = 2.1 + 1 = 3.1 \end{equation*}
and so in this case m = 3 and r = 0.1. Thus, the percentile will lie between \(y_3 = 54\) and \(y_4 = 64\) and much closer to 54 than 64. Numerically
\begin{equation*} P^{0.42} = 0.9 \cdot 54 + 0.1 \cdot 64 = 55. \end{equation*}
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