# `stats._binned_statistic`¶

## Module Contents¶

### Functions¶

 `binned_statistic`(x,values,statistic=”mean”,bins=10,range=None) Compute a binned statistic for one or more sets of data. `binned_statistic_2d`(x,y,values,statistic=”mean”,bins=10,range=None,expand_binnumbers=False) Compute a bidimensional binned statistic for one or more sets of data. `binned_statistic_dd`(sample,values,statistic=”mean”,bins=10,range=None,expand_binnumbers=False) Compute a multidimensional binned statistic for a set of data.
`binned_statistic`(x, values, statistic="mean", bins=10, range=None)

Compute a binned statistic for one or more sets of data.

This is a generalization of a histogram function. A histogram divides the space into bins, and returns the count of the number of points in each bin. This function allows the computation of the sum, mean, median, or other statistic of the values (or set of values) within each bin.

x : (N,) array_like
A sequence of values to be binned.
values : (N,) array_like or list of (N,) array_like
The data on which the statistic will be computed. This must be the same shape as x, or a set of sequences - each the same shape as x. If values is a set of sequences, the statistic will be computed on each independently.
statistic : string or callable, optional

The statistic to compute (default is ‘mean’). The following statistics are available:

• ‘mean’ : compute the mean of values for points within each bin. Empty bins will be represented by NaN.
• ‘median’ : compute the median of values for points within each bin. Empty bins will be represented by NaN.
• ‘count’ : compute the count of points within each bin. This is identical to an unweighted histogram. values array is not referenced.
• ‘sum’ : compute the sum of values for points within each bin. This is identical to a weighted histogram.
• ‘min’ : compute the minimum of values for points within each bin. Empty bins will be represented by NaN.
• ‘max’ : compute the maximum of values for point within each bin. Empty bins will be represented by NaN.
• function : a user-defined function which takes a 1D array of values, and outputs a single numerical statistic. This function will be called on the values in each bin. Empty bins will be represented by function([]), or NaN if this returns an error.
bins : int or sequence of scalars, optional
If bins is an int, it defines the number of equal-width bins in the given range (10 by default). If bins is a sequence, it defines the bin edges, including the rightmost edge, allowing for non-uniform bin widths. Values in x that are smaller than lowest bin edge are assigned to bin number 0, values beyond the highest bin are assigned to `bins[-1]`. If the bin edges are specified, the number of bins will be, (nx = len(bins)-1).
range : (float, float) or [(float, float)], optional
The lower and upper range of the bins. If not provided, range is simply `(x.min(), x.max())`. Values outside the range are ignored.
statistic : array
The values of the selected statistic in each bin.
bin_edges : array of dtype float
Return the bin edges `(length(statistic)+1)`.
binnumber: 1-D ndarray of ints
Indices of the bins (corresponding to bin_edges) in which each value of x belongs. Same length as values. A binnumber of i means the corresponding value is between (bin_edges[i-1], bin_edges[i]).

numpy.digitize, numpy.histogram, binned_statistic_2d, binned_statistic_dd

All but the last (righthand-most) bin is half-open. In other words, if bins is `[1, 2, 3, 4]`, then the first bin is `[1, 2)` (including 1, but excluding 2) and the second `[2, 3)`. The last bin, however, is `[3, 4]`, which includes 4.

New in version 0.11.0.

```>>> from scipy import stats
>>> import matplotlib.pyplot as plt
```

First some basic examples:

Create two evenly spaced bins in the range of the given sample, and sum the corresponding values in each of those bins:

```>>> values = [1.0, 1.0, 2.0, 1.5, 3.0]
>>> stats.binned_statistic([1, 1, 2, 5, 7], values, 'sum', bins=2)
(array([ 4. ,  4.5]), array([ 1.,  4.,  7.]), array([1, 1, 1, 2, 2]))
```

Multiple arrays of values can also be passed. The statistic is calculated on each set independently:

```>>> values = [[1.0, 1.0, 2.0, 1.5, 3.0], [2.0, 2.0, 4.0, 3.0, 6.0]]
>>> stats.binned_statistic([1, 1, 2, 5, 7], values, 'sum', bins=2)
(array([[ 4. ,  4.5], [ 8. ,  9. ]]), array([ 1.,  4.,  7.]),
array([1, 1, 1, 2, 2]))
```
```>>> stats.binned_statistic([1, 2, 1, 2, 4], np.arange(5), statistic='mean',
...                        bins=3)
(array([ 1.,  2.,  4.]), array([ 1.,  2.,  3.,  4.]),
array([1, 2, 1, 2, 3]))
```

As a second example, we now generate some random data of sailing boat speed as a function of wind speed, and then determine how fast our boat is for certain wind speeds:

```>>> windspeed = 8 * np.random.rand(500)
>>> boatspeed = .3 * windspeed**.5 + .2 * np.random.rand(500)
>>> bin_means, bin_edges, binnumber = stats.binned_statistic(windspeed,
...                 boatspeed, statistic='median', bins=[1,2,3,4,5,6,7])
>>> plt.figure()
>>> plt.plot(windspeed, boatspeed, 'b.', label='raw data')
>>> plt.hlines(bin_means, bin_edges[:-1], bin_edges[1:], colors='g', lw=5,
...            label='binned statistic of data')
>>> plt.legend()
```

Now we can use `binnumber` to select all datapoints with a windspeed below 1:

```>>> low_boatspeed = boatspeed[binnumber == 0]
```

As a final example, we will use `bin_edges` and `binnumber` to make a plot of a distribution that shows the mean and distribution around that mean per bin, on top of a regular histogram and the probability distribution function:

```>>> x = np.linspace(0, 5, num=500)
>>> x_pdf = stats.maxwell.pdf(x)
>>> samples = stats.maxwell.rvs(size=10000)
```
```>>> bin_means, bin_edges, binnumber = stats.binned_statistic(x, x_pdf,
...         statistic='mean', bins=25)
>>> bin_width = (bin_edges - bin_edges)
>>> bin_centers = bin_edges[1:] - bin_width/2
```
```>>> plt.figure()
>>> plt.hist(samples, bins=50, normed=True, histtype='stepfilled',
...          alpha=0.2, label='histogram of data')
>>> plt.plot(x, x_pdf, 'r-', label='analytical pdf')
>>> plt.hlines(bin_means, bin_edges[:-1], bin_edges[1:], colors='g', lw=2,
...            label='binned statistic of data')
>>> plt.plot((binnumber - 0.5) * bin_width, x_pdf, 'g.', alpha=0.5)
>>> plt.legend(fontsize=10)
>>> plt.show()
```
`binned_statistic_2d`(x, y, values, statistic="mean", bins=10, range=None, expand_binnumbers=False)

Compute a bidimensional binned statistic for one or more sets of data.

This is a generalization of a histogram2d function. A histogram divides the space into bins, and returns the count of the number of points in each bin. This function allows the computation of the sum, mean, median, or other statistic of the values (or set of values) within each bin.

x : (N,) array_like
A sequence of values to be binned along the first dimension.
y : (N,) array_like
A sequence of values to be binned along the second dimension.
values : (N,) array_like or list of (N,) array_like
The data on which the statistic will be computed. This must be the same shape as x, or a list of sequences - each with the same shape as x. If values is such a list, the statistic will be computed on each independently.
statistic : string or callable, optional

The statistic to compute (default is ‘mean’). The following statistics are available:

• ‘mean’ : compute the mean of values for points within each bin. Empty bins will be represented by NaN.
• ‘median’ : compute the median of values for points within each bin. Empty bins will be represented by NaN.
• ‘count’ : compute the count of points within each bin. This is identical to an unweighted histogram. values array is not referenced.
• ‘sum’ : compute the sum of values for points within each bin. This is identical to a weighted histogram.
• ‘min’ : compute the minimum of values for points within each bin. Empty bins will be represented by NaN.
• ‘max’ : compute the maximum of values for point within each bin. Empty bins will be represented by NaN.
• function : a user-defined function which takes a 1D array of values, and outputs a single numerical statistic. This function will be called on the values in each bin. Empty bins will be represented by function([]), or NaN if this returns an error.
bins : int or [int, int] or array_like or [array, array], optional

The bin specification:

• the number of bins for the two dimensions (nx = ny = bins),
• the number of bins in each dimension (nx, ny = bins),
• the bin edges for the two dimensions (x_edge = y_edge = bins),
• the bin edges in each dimension (x_edge, y_edge = bins).

If the bin edges are specified, the number of bins will be, (nx = len(x_edge)-1, ny = len(y_edge)-1).

range : (2,2) array_like, optional
The leftmost and rightmost edges of the bins along each dimension (if not specified explicitly in the bins parameters): [[xmin, xmax], [ymin, ymax]]. All values outside of this range will be considered outliers and not tallied in the histogram.
expand_binnumbers : bool, optional

‘False’ (default): the returned binnumber is a shape (N,) array of linearized bin indices. ‘True’: the returned binnumber is ‘unraveled’ into a shape (2,N) ndarray, where each row gives the bin numbers in the corresponding dimension. See the binnumber returned value, and the Examples section.

New in version 0.17.0.

statistic : (nx, ny) ndarray
The values of the selected statistic in each two-dimensional bin.
x_edge : (nx + 1) ndarray
The bin edges along the first dimension.
y_edge : (ny + 1) ndarray
The bin edges along the second dimension.
binnumber : (N,) array of ints or (2,N) ndarray of ints
This assigns to each element of sample an integer that represents the bin in which this observation falls. The representation depends on the expand_binnumbers argument. See Notes for details.

numpy.digitize, numpy.histogram2d, binned_statistic, binned_statistic_dd

Binedges: All but the last (righthand-most) bin is half-open. In other words, if bins is `[1, 2, 3, 4]`, then the first bin is `[1, 2)` (including 1, but excluding 2) and the second `[2, 3)`. The last bin, however, is `[3, 4]`, which includes 4.

binnumber: This returned argument assigns to each element of sample an integer that represents the bin in which it belongs. The representation depends on the expand_binnumbers argument. If ‘False’ (default): The returned binnumber is a shape (N,) array of linearized indices mapping each element of sample to its corresponding bin (using row-major ordering). If ‘True’: The returned binnumber is a shape (2,N) ndarray where each row indicates bin placements for each dimension respectively. In each dimension, a binnumber of i means the corresponding value is between (D_edge[i-1], D_edge[i]), where ‘D’ is either ‘x’ or ‘y’.

New in version 0.11.0.

```>>> from scipy import stats
```

Calculate the counts with explicit bin-edges:

```>>> x = [0.1, 0.1, 0.1, 0.6]
>>> y = [2.1, 2.6, 2.1, 2.1]
>>> binx = [0.0, 0.5, 1.0]
>>> biny = [2.0, 2.5, 3.0]
>>> ret = stats.binned_statistic_2d(x, y, None, 'count', bins=[binx,biny])
>>> ret.statistic
array([[ 2.,  1.],
[ 1.,  0.]])
```

The bin in which each sample is placed is given by the binnumber returned parameter. By default, these are the linearized bin indices:

```>>> ret.binnumber
array([5, 6, 5, 9])
```

The bin indices can also be expanded into separate entries for each dimension using the expand_binnumbers parameter:

```>>> ret = stats.binned_statistic_2d(x, y, None, 'count', bins=[binx,biny],
...                                 expand_binnumbers=True)
>>> ret.binnumber
array([[1, 1, 1, 2],
[1, 2, 1, 1]])
```

Which shows that the first three elements belong in the xbin 1, and the fourth into xbin 2; and so on for y.

`binned_statistic_dd`(sample, values, statistic="mean", bins=10, range=None, expand_binnumbers=False)

Compute a multidimensional binned statistic for a set of data.

This is a generalization of a histogramdd function. A histogram divides the space into bins, and returns the count of the number of points in each bin. This function allows the computation of the sum, mean, median, or other statistic of the values within each bin.

sample : array_like
Data to histogram passed as a sequence of D arrays of length N, or as an (N,D) array.
values : (N,) array_like or list of (N,) array_like
The data on which the statistic will be computed. This must be the same shape as x, or a list of sequences - each with the same shape as x. If values is such a list, the statistic will be computed on each independently.
statistic : string or callable, optional

The statistic to compute (default is ‘mean’). The following statistics are available:

• ‘mean’ : compute the mean of values for points within each bin. Empty bins will be represented by NaN.
• ‘median’ : compute the median of values for points within each bin. Empty bins will be represented by NaN.
• ‘count’ : compute the count of points within each bin. This is identical to an unweighted histogram. values array is not referenced.
• ‘sum’ : compute the sum of values for points within each bin. This is identical to a weighted histogram.
• ‘min’ : compute the minimum of values for points within each bin. Empty bins will be represented by NaN.
• ‘max’ : compute the maximum of values for point within each bin. Empty bins will be represented by NaN.
• function : a user-defined function which takes a 1D array of values, and outputs a single numerical statistic. This function will be called on the values in each bin. Empty bins will be represented by function([]), or NaN if this returns an error.
bins : sequence or int, optional

The bin specification must be in one of the following forms:

• A sequence of arrays describing the bin edges along each dimension.
• The number of bins for each dimension (nx, ny, … = bins).
• The number of bins for all dimensions (nx = ny = … = bins).
range : sequence, optional
A sequence of lower and upper bin edges to be used if the edges are not given explicitely in bins. Defaults to the minimum and maximum values along each dimension.
expand_binnumbers : bool, optional

‘False’ (default): the returned binnumber is a shape (N,) array of linearized bin indices. ‘True’: the returned binnumber is ‘unraveled’ into a shape (D,N) ndarray, where each row gives the bin numbers in the corresponding dimension. See the binnumber returned value, and the Examples section of binned_statistic_2d.

New in version 0.17.0.

statistic : ndarray, shape(nx1, nx2, nx3,…)
The values of the selected statistic in each two-dimensional bin.
bin_edges : list of ndarrays
A list of D arrays describing the (nxi + 1) bin edges for each dimension.
binnumber : (N,) array of ints or (D,N) ndarray of ints
This assigns to each element of sample an integer that represents the bin in which this observation falls. The representation depends on the expand_binnumbers argument. See Notes for details.

numpy.digitize, numpy.histogramdd, binned_statistic, binned_statistic_2d

Binedges: All but the last (righthand-most) bin is half-open in each dimension. In other words, if bins is `[1, 2, 3, 4]`, then the first bin is `[1, 2)` (including 1, but excluding 2) and the second `[2, 3)`. The last bin, however, is `[3, 4]`, which includes 4.

binnumber: This returned argument assigns to each element of sample an integer that represents the bin in which it belongs. The representation depends on the expand_binnumbers argument. If ‘False’ (default): The returned binnumber is a shape (N,) array of linearized indices mapping each element of sample to its corresponding bin (using row-major ordering). If ‘True’: The returned binnumber is a shape (D,N) ndarray where each row indicates bin placements for each dimension respectively. In each dimension, a binnumber of i means the corresponding value is between (bin_edges[D][i-1], bin_edges[D][i]), for each dimension ‘D’.

New in version 0.11.0.