Question

find the value corresponding to the 25th percentile. the scores are below. 18, 15, 12, 6, 8, 2, 3, 5, 20, 10

Explanation:

Step1: Sort the data

$2,3,5,6,8,10,12,15,18,20$

Step2: Calculate the index

$n = 10$, $p=0.25$. Index $i=np = 10\times0.25=2.5$.

Step3: Interpolate

Since $i$ is not an integer, we interpolate between the 2nd and 3rd - ordered values. The 2nd - ordered value is $3$ and the 3rd - ordered value is $5$. The 25th percentile is $3+(5 - 3)\times(2.5 - 2)=3 + 1=4$. Since $4$ is not in the given options, the answer is "None of the above".

Answer:

None of the above