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.
Let's follow the steps given below
- Arrange the data in ascending order.
- 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.
- 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.
- If more than one value falls in the 90th place, their average is taken.
- 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.