Question

question 6
calculate the 20th percentile of the data shown
x
3.6
4.4
6.1
10.4
14.1
17
19.2
22.1
23.6
24.2

Explanation:

Step1: Determine the number of data points

The data set has \( n = 10 \) values (3.6, 4.4, 6.1, 10.4, 14.1, 17, 19.2, 22.1, 23.6, 24.2).

Step2: Calculate the index \( i \)

The formula for the index \( i \) of the \( p \)-th percentile is \( i=\frac{p}{100}\times n \). For \( p = 20 \) and \( n = 10 \), we have \( i=\frac{20}{100}\times10 = 2 \).

Step3: Check if \( i \) is an integer

Since \( i = 2 \) is an integer, the 20th percentile is the average of the \( i \)-th and \( (i + 1) \)-th values in the sorted data. The sorted data is already in order. The 2nd value is 4.4 and the 3rd value is 6.1.

Step4: Calculate the average

The average is \( \frac{4.4+6.1}{2}=\frac{10.5}{2}=5.25 \).

Answer:

5.25