What is a Fractile in Statistics?

Fractile is a term used in statistics to describe the fraction of observations that fall below a given quantile. In other words, it is the proportion of data points that are below a certain percentage of the total data.

For example, if we have a dataset of exam scores and we want to know what percentage of students scored below the 25th percentile, we can calculate the fractile as follows:

1. Sort the data in ascending order.
2. Find the 25th percentile (i.e., the value below which 25% of the data falls).
3. Count the number of observations that are below the 25th percentile.
4. Divide the number of observations below the 25th percentile by the total number of observations to get the fractile.

The fractile can be expressed as a percentage, like this: "25% of the students scored below the 25th percentile."

Fractiles can be used in a variety of ways in statistics and data analysis, such as:

* Describing the distribution of a dataset: By looking at the fractiles, we can get a sense of how many observations are below certain percentiles, which can help us understand the overall shape of the distribution.
* Identifying outliers: If an observation is significantly far from the median or other percentiles, it may be considered an outlier and should be investigated further.
* Comparing datasets: We can use fractiles to compare the distribution of different datasets and look for differences or similarities between them.

I hope this helps! Let me know if you have any more questions.