def quantile(
        self,
        q: ArrayLike,
        dim: Dims = None,
        *,
        method: QuantileMethods = "linear",
        keep_attrs: bool | None = None,
        skipna: bool | None = None,
        interpolation: QuantileMethods | None = None,
    ) -> T_Xarray:
        """Compute the qth quantile over each array in the groups and
        concatenate them together into a new array.

        Parameters
        ----------
        q : float or sequence of float
            Quantile to compute, which must be between 0 and 1
            inclusive.
        dim : str or Iterable of Hashable, optional
            Dimension(s) over which to apply quantile.
            Defaults to the grouped dimension.
        method : str, default: "linear"
            This optional parameter specifies the interpolation method to use when the
            desired quantile lies between two data points. The options sorted by their R
            type as summarized in the H&F paper [1]_ are:

                1. "inverted_cdf"
                2. "averaged_inverted_cdf"
                3. "closest_observation"
                4. "interpolated_inverted_cdf"
                5. "hazen"
                6. "weibull"
                7. "linear"  (default)
                8. "median_unbiased"
                9. "normal_unbiased"

            The first three methods are discontiuous.  The following discontinuous
            variations of the default "linear" (7.) option are also available:

                * "lower"
                * "higher"
                * "midpoint"
                * "nearest"

            See :py:func:`numpy.quantile` or [1]_ for details. The "method" argument
            was previously called "interpolation", renamed in accordance with numpy
            version 1.22.0.
        keep_attrs : bool or None, default: None
            If True, the dataarray's attributes (`attrs`) will be copied from
            the original object to the new one.  If False, the new
            object will be returned without attributes.
        skipna : bool or None, default: None
            If True, skip missing values (as marked by NaN). By default, only
            skips missing values for float dtypes; other dtypes either do not
            have a sentinel missing value (int) or skipna=True has not been
            implemented (object, datetime64 or timedelta64).

        Returns
        -------
        quantiles : Variable
            If `q` is a single quantile, then the result is a
            scalar. If multiple percentiles are given, first axis of
            the result corresponds to the quantile. In either case a
            quantile dimension is added to the return array. The other
            dimensions are the dimensions that remain after the
            reduction of the array.

        See Also
        --------
        numpy.nanquantile, numpy.quantile, pandas.Series.quantile, Dataset.quantile
        DataArray.quantile

        Examples
        --------
        >>> da = xr.DataArray(
        ...     [[1.3, 8.4, 0.7, 6.9], [0.7, 4.2, 9.4, 1.5], [6.5, 7.3, 2.6, 1.9]],
        ...     coords={"x": [0, 0, 1], "y": [1, 1, 2, 2]},
        ...     dims=("x", "y"),
        ... )
        >>> ds = xr.Dataset({"a": da})
        >>> da.groupby("x").quantile(0)
        <xarray.DataArray (x: 2, y: 4)> Size: 64B
        array([[0.7, 4.2, 0.7, 1.5],
               [6.5, 7.3, 2.6, 1.9]])
        Coordinates:
          * y         (y) int64 32B 1 1 2 2
            quantile  float64 8B 0.0
          * x         (x) int64 16B 0 1
        >>> ds.groupby("y").quantile(0, dim=...)
        <xarray.Dataset> Size: 40B
        Dimensions:   (y: 2)
        Coordinates:
            quantile  float64 8B 0.0
          * y         (y) int64 16B 1 2
        Data variables:
            a         (y) float64 16B 0.7 0.7
        >>> da.groupby("x").quantile([0, 0.5, 1])
        <xarray.DataArray (x: 2, y: 4, quantile: 3)> Size: 192B
        array([[[0.7 , 1.  , 1.3 ],
                [4.2 , 6.3 , 8.4 ],
                [0.7 , 5.05, 9.4 ],
                [1.5 , 4.2 , 6.9 ]],
        <BLANKLINE>
               [[6.5 , 6.5 , 6.5 ],
                [7.3 , 7.3 , 7.3 ],
                [2.6 , 2.6 , 2.6 ],
                [1.9 , 1.9 , 1.9 ]]])
        Coordinates:
          * y         (y) int64 32B 1 1 2 2
          * quantile  (quantile) float64 24B 0.0 0.5 1.0
          * x         (x) int64 16B 0 1
        >>> ds.groupby("y").quantile([0, 0.5, 1], dim=...)
        <xarray.Dataset> Size: 88B
        Dimensions:   (y: 2, quantile: 3)
        Coordinates:
          * quantile  (quantile) float64 24B 0.0 0.5 1.0
          * y         (y) int64 16B 1 2
        Data variables:
            a         (y, quantile) float64 48B 0.7 5.35 8.4 0.7 2.25 9.4

        References
        ----------
        .. [1] R. J. Hyndman and Y. Fan,
           "Sample quantiles in statistical packages,"
           The American Statistician, 50(4), pp. 361-365, 1996
        """
        # Dataset.quantile does this, do it for flox to ensure same output.
        q = np.asarray(q, dtype=np.float64)

        if (
            method == "linear"
            and OPTIONS["use_flox"]
            and contains_only_chunked_or_numpy(self._obj)
            and module_available("flox", minversion="0.9.4")
        ):
            result = self._flox_reduce(
                func="quantile", q=q, dim=dim, keep_attrs=keep_attrs, skipna=skipna
            )
            return result
        else:
            if dim is None:
                dim = (self._group_dim,)
            return self.map(
                self._obj.__class__.quantile,
                shortcut=False,
                q=q,
                dim=dim or self._group_dim,
                method=method,
                keep_attrs=keep_attrs,
                skipna=skipna,
                interpolation=interpolation,
            )
Compute the qth quantile over each array in the groups and
        concatenate them together into a new array.

        Parameters
        ----------
        q : float or sequence of float
            Quantile to compute, which must be between 0 and 1
            inclusive.
        dim : str or Iterable of Hashable, optional
            Dimension(s) over which to apply quantile.
            Defaults to the grouped dimension.
        method : str, default: "linear"
            This optional parameter specifies the interpolation method to use when the
            desired quantile lies between two data points. The options sorted by their R
            type as summarized in the H&F paper [1]_ are:

                1. "inverted_cdf"
                2. "averaged_inverted_cdf"
                3. "closest_observation"
                4. "interpolated_inverted_cdf"
                5. "hazen"
                6. "weibull"
                7. "linear"  (default)
                8. "median_unbiased"
                9. "normal_unbiased"

            The first three methods are discontiuous.  The following discontinuous
            variations of the default "linear" (7.) option are also available:

                * "lower"
                * "higher"
                * "midpoint"
                * "nearest"

            See :py:func:`numpy.quantile` or [1]_ for details. The "method" argument
            was previously called "interpolation", renamed in accordance with numpy
            version 1.22.0.
        keep_attrs : bool or None, default: None
            If True, the dataarray's attributes (`attrs`) will be copied from
            the original object to the new one.  If False, the new
            object will be returned without attributes.
        skipna : bool or None, default: None
            If True, skip missing values (as marked by NaN). By default, only
            skips missing values for float dtypes; other dtypes either do not
            have a sentinel missing value (int) or skipna=True has not been
            implemented (object, datetime64 or timedelta64).

        Returns
        -------
        quantiles : Variable
            If `q` is a single quantile, then the result is a
            scalar. If multiple percentiles are given, first axis of
            the result corresponds to the quantile. In either case a
            quantile dimension is added to the return array. The other
            dimensions are the dimensions that remain after the
            reduction of the array.

        See Also
        --------
        numpy.nanquantile, numpy.quantile, pandas.Series.quantile, Dataset.quantile
        DataArray.quantile

        Examples
        --------
        >>> da = xr.DataArray(
        ...     [[1.3, 8.4, 0.7, 6.9], [0.7, 4.2, 9.4, 1.5], [6.5, 7.3, 2.6, 1.9]],
        ...     coords={"x": [0, 0, 1], "y": [1, 1, 2, 2]},
        ...     dims=("x", "y"),
        ... )
        >>> ds = xr.Dataset({"a": da})
        >>> da.groupby("x").quantile(0)
        <xarray.DataArray (x: 2, y: 4)> Size: 64B
        array([[0.7, 4.2, 0.7, 1.5],
               [6.5, 7.3, 2.6, 1.9]])
        Coordinates:
          * y         (y) int64 32B 1 1 2 2
            quantile  float64 8B 0.0
          * x         (x) int64 16B 0 1
        >>> ds.groupby("y").quantile(0, dim=...)
        <xarray.Dataset> Size: 40B
        Dimensions:   (y: 2)
        Coordinates:
            quantile  float64 8B 0.0
          * y         (y) int64 16B 1 2
        Data variables:
            a         (y) float64 16B 0.7 0.7
        >>> da.groupby("x").quantile([0, 0.5, 1])
        <xarray.DataArray (x: 2, y: 4, quantile: 3)> Size: 192B
        array([[[0.7 , 1.  , 1.3 ],
                [4.2 , 6.3 , 8.4 ],
                [0.7 , 5.05, 9.4 ],
                [1.5 , 4.2 , 6.9 ]],
        <BLANKLINE>
               [[6.5 , 6.5 , 6.5 ],
                [7.3 , 7.3 , 7.3 ],
                [2.6 , 2.6 , 2.6 ],
                [1.9 , 1.9 , 1.9 ]]])
        Coordinates:
          * y         (y) int64 32B 1 1 2 2
          * quantile  (quantile) float64 24B 0.0 0.5 1.0
          * x         (x) int64 16B 0 1
        >>> ds.groupby("y").quantile([0, 0.5, 1], dim=...)
        <xarray.Dataset> Size: 88B
        Dimensions:   (y: 2, quantile: 3)
        Coordinates:
          * quantile  (quantile) float64 24B 0.0 0.5 1.0
          * y         (y) int64 16B 1 2
        Data variables:
            a         (y, quantile) float64 48B 0.7 5.35 8.4 0.7 2.25 9.4

        References
        ----------
        .. [1] R. J. Hyndman and Y. Fan,
           "Sample quantiles in statistical packages,"
           The American Statistician, 50(4), pp. 361-365, 1996
        
xarray/core/groupby.py