# FAQ: Quantiles - Quantiles in NumPy

This community-built FAQ covers the “Quantiles in NumPy” exercise from the lesson “Quantiles”.

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## FAQs on the exercise Quantiles in NumPy

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``````import numpy as np

dataset = [5, 10, -20, 42, -9, 10]
ten_percent = np.quantile(dataset, 0.10)   # -14.5
``````

For those who wondered why `ten_percent` holds the value `-14.5`, I would like to share my research about `numpy.quantile()`, based on the documentation.

The documentation has the following Notes:

Given a vector `V` of length `N` , the q-th quantile of `V` is the value `q` of the way from the minimum to the maximum in a sorted copy of `V` . The values and distances of the two nearest neighbors as well as the interpolation parameter will determine the quantile if the normalized ranking does not match the location of `q` exactly. This function is the same as the median if `q=0.5` , the same as the minimum if `q=0.0` and the same as the maximum if `q=1.0` .

The default setting for the `interpolation` parameter is `linear` :

interpolation {‘linear’, ‘lower’, ‘higher’, ‘midpoint’, ‘nearest’}
This optional parameter specifies the interpolation method to use when the desired quantile lies between two data points `i < j` :

• linear: `i + (j - i) * fraction` , where `fraction` is the fractional part of the index surrounded by `i` and `j` .

Now consider `dataset` in the example code at the beginning. Since the length is 6, quantiles at 0%, 20%, 40%, 60%, 80%, and 100% are exactly determined:

0%: -20
20%: -9
40%: 5
60%: 10
80%: 10
100%: 42

Other quantiles are interpolated linearly. For example, 10% falls between 0% and 20%, so the quantile at 10% will be

-20 + (-9 - (-20)) * fraction.

Here, fraction = 10 / 20 = 0.5, so it is

-20 + (-9 - (-20)) * 0.5 = -14.5.

We may find it easier to understand by drawing the graph as follows:

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