Question

question 20
calculate the 30th percentile of the data shown
x
2.3
3.5
5.6
13.7
17.9
18.9
21.5
25.2
28
29.5

Explanation:

Step1: Arrange data in ascending order (already in ascending order)

The data set is $2.3,3.5,5.6,13.7,17.9,18.9,21.5,25.2,28,29.5$. There are $n = 10$ data - points.

Step2: Calculate the index

Use the formula $i=\frac{p}{100}\times n$, where $p = 30$ and $n = 10$. So $i=\frac{30}{100}\times10=3$.

Step3: Determine the percentile value

Since $i$ is an integer, the $p$ - th percentile is the average of the $i$ - th and $(i + 1)$ - th ordered data values. The 3rd value is $5.6$ and the 4th value is $13.7$. The 30th percentile $P_{30}=\frac{5.6 + 13.7}{2}=\frac{19.3}{2}=9.65$.

Answer:

$9.65$