Percentiles

Different directions to same data

• Percentile Rank- We had the set of data and we find out what percentile is a particular data is. This is what we did while calculating exam scores.

• Percentile - Here, we know the percentile rank and we want to find out the actual value behind it. That's to get the actual score of the student. This is represented using the notation - $p{95}$.

Percentiles are calculated by sorting the data and then find the number of data points that are less than the value we're interested in. The formula for calculating the percentile rank of a value is:

$$\begin{aligned} \text{percentile rank} = \frac{\text{Number of values less or equal to the value}}{\text{Total number of values}} * 100 \end{aligned}$$

Using percentiles in system design

When they mention p95, they're referring to the percentile rank. Meaning the data is already sorted and they already picked the actual value that has 95% of the data points below it.

Example about the p95 latency

A service's response time is measures and sorted. Meaning the fastest response time is at the beginning and the slowest response time is at the end.

Now if they say p95, it means the actual value that has 95% of the response times below it.

translation between percentile rank and value

When they say p95, they're referring to the percentile rank.

But when they say $95^{\text{th}}$ percentile, they're referring to the value that has 95% of the data points below it.

Median is the $50^{\text{th}}$ percentile

Median is also a special case of percentile. Median is just the value that has 50% of the data points below it.