For the distribution in the following table,what is the 90^th percentile? $$\begin{array} { c c } \mathrm { X } & \mathrm { c } \% \ 9 & 100 \% \ 8 & 80 \% \ 7 & 50 \% \ 6 & 25 \% \ \hline \end{array}$$ A)X = 9.5? B)?X = 9 C)?X = 8.5 D)?X = 8

Question

Quizplus · Accepted Answer

The 90th percentile implies that 90% of the data is below the value at the 90th percentile. From the table, we can see that 80% of the data is below the value 8, and 100% of the data is below 9. So, the value at the 90th percentile must be between 8 and 9, since only 10% of the data is between those two values. The 90th percentile splits this 10% into two parts - 5% above the value at the 90th percentile and 5% below. Since the percentage of data between 8 and 9 is not evenly distributed, we can estimate that the value at the 90th percentile is closer to 9 than to 8. Therefore, the best choice is B) X = 9.

For the Distribution in the Following Table,what Is the 90th Xc%9100%880%750%625%\begin{array} { c c } \mathrm { X } & \mathrm { c } \% \\9 & 100 \% \\8 & 80 \% \\7 & 50 \% \\6 & 25 \% \\\hline\end{array}X9876​c%100%80%50%25%​​

For the Distribution in the Following Table,what Is the 90^th $\begin{array} { c c } \mathrm { X } & \mathrm { c } \% \\9 & 100 \% \\8 & 80 \% \\7 & 50 \% \\6 & 25 \% \\\hline\end{array}$