Reading response time percentile in Designing Data-Intensive Applications Book

Question

In the book Designing Data-Intensive Applications, there is this sentence:

For example, if the 95th percentile response time is 1.5 seconds, that means 95 out of 100 requests take less than 1.5 seconds, and 5 out of 100 requests take 1.5 seconds or more.

The confusing part is the saying that 95 of these requests will take less than 1.5 seconds. Isn't that supposed to be that 95 of requests take 1.5 seconds or less, and the remaining 5 takes more than 1.5 seconds? Or, the one percent in the 95th percentile takes exactly 1.5 seconds, 89th percentile and below take less than 1.5, and the 96th and above percentiles take more than 1.5? What is the correct reading of these numbers?

I have done some research on this and found several articles. The interesting part is that some say what I say and some don't.

Some of the links that read the percentile similar to 95 of the requests take 1.5 or less:

• average 90th percentile response time and average response time

90% percentile is a statistical measurement, in case of JMeter it means that 90% of the sampler response times were smaller than or equal to this time

• https://www.dynatrace.com/news/blog/why-averages-suck-and-percentiles-are-great/

so 90 percent of the requests are processed in 3.0 seconds or less

• https://www.adfpm.com/adf-performance-monitor-monitoring-with-percentiles

If the 90th percentile of the same transaction is at 1000ms it means that 90% are as fast or faster and only 10% are slower.

Other links that read the percentile similar to 95 of the requests take less than 1.5:

• https://www.elastic.co/blog/averages-can-dangerous-use-percentile

In contrast, the 99th percentile says “99% of your values are less than 850ms”, which is a very different picture.

Answer 1

I got the answer from this website and according to them, both of them is true. It just depends on how the percentile rank is calculated:

The word “percentile” is used informally in the above definition. In common use, the percentile usually indicates that a certain percentage falls below that percentile. For example, if you score in the 25th percentile, then 25% of test takers are below your score. The “25” is called the percentile rank. In statistics, it can get a little more complicated as there are actually three definitions of “percentile.” Here are the first two (see below for definition 3), based on an arbitrary “25th percentile”:

Definition 1: The nth percentile is the lowest score that is greater than a certain percentage (“n”) of the scores. In this example, or n is 25, so we’re looking for the lowest score that is greater than 25%.

Definition 2: The nth percentile is the smallest score that is greater than or equal to a certain percentage of the scores. To rephrase this, it’s the percentage of data that falls at or below a certain observation. This is the definition used in AP statistics. In this example, the 25th percentile is the score that’s greater or equal to 25% of the scores.