Find the values of the 30th and 90th percentiles of the data. 18,9,7,5,11,7,17,20,19,2,17,12,5,1,13,12,11,15,16,20

A percentile is defined as a number where a certain percentage of scores fall below that number. The 25th percentile is also called the first quartile.

Answer: The values of the 30th and 90th percentiles of the data are 7 and 19.

Let us proceed step by step.

Explanation:

Let's follow the steps given below

1. Arrange the data in ascending order.
2. The 30th percentile of a data set is the data value that appeared in the 30th position after the dataset has been divided into 100 equal parts.
3. Thus to find the 30th percentile of a dataset, we first divide the dataset into 100 equal parts, and then the data value in the 30th place is the 30th percentile of the dataset.
4. If more than one value falls in the 90th place, their average is taken.
5. We need to repeat the same process for the 90th percentile.

Given data: 1,2,5,5,7,7,9,11,11,12,12,13,15,16,17,17,18,19,20,20

Since there are 20 numbers in the data. So, 30% of 20 = 6 and 90% of 20 = 18

Hence, 6th term will be 7 and the 18th term will be 19.

Therefore, the values of the 30th and 90th percentiles of the data are 7 and 19.