Question

calculate the 55th percentile of the data shown
x
2.5
4.4
13.5
14.7
28.3

Explanation:

Step1: Sort the data (already sorted)

The data is $2.5, 4.4, 13.5, 14.7, 28.3$.

Step2: Calculate the index

The formula for the index $i$ of the $p$ - th percentile is $i=\frac{p}{100}\times n$, where $p = 55$ and $n = 5$. So $i=\frac{55}{100}\times5=2.75$.

Step3: Interpolate

Since the index is not an integer, we interpolate. Let $k$ be the integer part of $i$ ($k = 2$) and $f$ be the fractional part ($f=0.75$). The $k$ - th value is $x_k = 4.4$ and the $(k + 1)$ - th value is $x_{k+1}=13.5$. The formula for interpolation is $P_p=x_k+f\times(x_{k + 1}-x_k)$. So $P_{55}=4.4+0.75\times(13.5 - 4.4)=4.4+0.75\times9.1=4.4 + 6.825=11.225$.

Answer:

$11.225$