percentil no. $$$99$$$ de $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$
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Encuentre el percentil no. $$$99$$$ de $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$.
Solución
El percentil nro. $$$p$$$ es un valor tal que al menos $$$p$$$ por ciento de las observaciones es menor o igual a este valor y al menos $$$100 - p$$$ por ciento de las observaciones es mayor o igual a este valor.
El primer paso es ordenar los valores.
Los valores ordenados son $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$1$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$, $$$400$$$.
Como hay $$$200$$$ valores, entonces $$$n = 200$$$.
Ahora, calcula el índice: $$$i = \frac{p}{100} n = \frac{99}{100} \cdot 200 = 198$$$.
Dado que el índice $$$i$$$ es un número entero, el percentil no. $$$99$$$ es el promedio de los valores en las posiciones $$$i$$$ y $$$i + 1$$$.
El valor en la posición $$$i = 198$$$ es $$$400$$$ ; el valor en la posición $$$i + 1 = 199$$$ es $$$400$$$.
Su promedio es el percentil: $$$\frac{400 + 400}{2} = 400$$$.
Respuesta
El percentil nro. $$$99$$$A es $$$400$$$A.