you collected the following sample data: 18, 10, 12, 12, 15, 11. what is the percentile rank of 11? hint…

you collected the following sample data: 18, 10, 12, 12, 15, 11. what is the percentile rank of 11? hint: use the following. $s = sqrt{\frac{sum (x - \bar{x})^2}{n - 1}}$ $z=\frac{x - \bar{x}}{s}$ the z - table. 32% 28% 25% 19% 21%

you collected the following sample data: 18, 10, 12, 12, 15, 11. what is the percentile rank of 11? hint: use the following. $s = sqrt{\frac{sum (x - \bar{x})^2}{n - 1}}$ $z=\frac{x - \bar{x}}{s}$ the z - table. 32% 28% 25% 19% 21%

Answer

Explanation:

Step1: Sort the data

The sorted data is 10, 11, 12, 12, 15, 18.

Step2: Calculate the position of 11

There are 6 data - points. The number of data - points less than or equal to 11 is 2.

Step3: Calculate the percentile rank

The formula for percentile rank is $\text{Percentile Rank}=\frac{\text{Number of data points less than or equal to the value}}{\text{Total number of data points}}\times100%$. So, $\text{Percentile Rank}=\frac{2}{6}\times100%\approx 33.33%$. But if we use the more formal formula for percentile rank $PR=\frac{c + 0.5f}{n}\times100%$, where $c$ is the number of scores below the score of interest, $f$ is the frequency of the score of interest, and $n$ is the total number of scores. Here, $c = 1$, $f = 1$, $n=6$. Then $PR=\frac{1 + 0.5\times1}{6}\times100%=\frac{1.5}{6}\times100% = 25%$.

Answer:

25%