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# NumPy | quantile method

schedule Aug 12, 2023
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Numpy's `quantile(~)` method returns the interpolated value at the specified quantile. Note that this method is exactly the same as the `percentile(~)`, just that the `quantile(~)` method takes a value between 0 and 1 - not 0 and 100.

# Parameters

1. `a` | `array-like`

The input array.

2. `q` | `array-like` of `float`

The desired quantile to compute, which must be between 0 (inclusive) and 1 (inclusive).

3. `axis` | `None` or `int` | `optional`

The axis along which to compute the percentile. For 2D arrays, the allowed values are as follows:

Axis

Meaning

0

Compute the quantile column-wise

1

Compute the quantile row-wise

None

Compute the percentile on a flattened input array

By default, `axis=None`.

4. `out` | `Numpy array` | `optional`

Instead of creating a new array, you can place the computed result into the array specified by `out`.

5. `overwrite_input` | `boolean` | `optional`

Whether to save intermediate calculations to the input array `a`. This would save memory space, but would also make the content of `a` undefined. By default, `overwrite_input=False`.

6. `interpolation`link | `string` | `optional`

How the values are interpolated when the given percentile sits between two data-points, say `i` and `j` where `i<j`:

Value

Meaning

linear

Standard linear interpolation

lower

Returns `i`

higher

Return `j`

midpoint

Returns `(i+j)/2`

nearest

Returns `i` or `j`, whichever is closer.

By default, `interpolation="linear"`.

# Return value

If `q` is a scalar, then a scalar is returned. Otherwise, a Numpy array is returned.

# Examples

## Computing a single percentile

To get the value at the 0.5 quantile:

``` a = np.array([5,6,7,8,9])np.quantile(a, 0.5) 7.0 ```

## Computing multiple percentiles

To get the values at the 50th and 75th percentiles:

``` a = np.array([5,6,7,8,9])np.quantile(a, [0.5, 0.75]) array([7., 8.]) ```

## Changing interpolation methods

### linear

Consider the case when the value corresponding to the specified quantile does not exist:

``` a = np.array([5,6,7,8,9])np.quantile(a, 0.45) # interpolation="linear" 6.800000000000001 ```

Here, since the value corresponding to the 45th percentile does not exist in the array, the value was linearly interpolated between 6 and 7.

### lower

``` a = np.array([5,6,7,8,9])np.quantile(a, 0.45, interpolation="lower") 6 ```

Again, since the 45% quantile does not exist, we need to perform interpolation. We know it is between the values 6 and 7. By passing in `"lower"`, we select the lower value, that is, 6 in this case.

### higher

``` a = np.array([5,6,7,8,9])np.quantile(a, 0.45, interpolation="higher") 7 ```

Same logic as `"lower"`, but we take the upper value.

### nearest

``` a = np.array([5,6,7,8,9])np.quantile(a, 0.45, interpolation="nearest") 7 ```

By passing in "nearest", instead of always selecting the lower or upper value, we take whichever is nearest. Here, judging from the output from when `interpolation="linear"`, we know that the interpolated value is closer to 7 rather than 6.

### midpoint

``` a = np.array([5,6,7,8,9])np.quantile(a, 0.45, interpolation="midpoint") 6.5 ```

Here, we just take the midpoint of the lower and upper value, so `(6+7)/2=6.5`.

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