Question

the 40th percentile of the data 5,8,10,11,13,14,18,19,20,21,23,25,26,30,31,32,33,35,37,39 is
36
6.5
24
10.5
31.5
19.5

Explanation:

Step1: Calculate the index

First, find the number of data points $n = 20$. Use the formula $i=\frac{p}{100}\times n$, where $p = 40$. So $i=\frac{40}{100}\times20=8$.

Step2: Determine the percentile

Since $i$ is an integer, the $p$ - th percentile is the average of the $i$ - th and $(i + 1)$ - th ordered data values. The 8th value is 19 and the 9th value is 20. The average is $\frac{19 + 20}{2}=19.5$.

Answer:

19.5