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<section id="numpy-average">
<h1>numpy.average<a class="headerlink" href="#numpy-average" title="Link to this heading">#</a></h1>
<dl class="py function">
<dt class="sig sig-object py" id="numpy.average">
<span class="sig-prename descclassname"><span class="pre">numpy.</span></span><span class="sig-name descname"><span class="pre">average</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">axis=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weights=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">returned=False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">keepdims=<no</span> <span class="pre">value></span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/main/numpy/lib/_function_base_impl.py#L413-L574"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#numpy.average" title="Link to this definition">#</a></dt>
<dd><p>Compute the weighted average along the specified axis.</p>
<dl class="field-list">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl>
<dt><strong>a</strong><span class="classifier">array_like</span></dt><dd><p>Array containing data to be averaged. If <em class="xref py py-obj">a</em> is not an array, a
conversion is attempted.</p>
</dd>
<dt><strong>axis</strong><span class="classifier">None or int or tuple of ints, optional</span></dt><dd><p>Axis or axes along which to average <em class="xref py py-obj">a</em>. The default,
<em class="xref py py-obj">axis=None</em>, will average over all of the elements of the input array.
If axis is negative it counts from the last to the first axis.
If axis is a tuple of ints, averaging is performed on all of the axes
specified in the tuple instead of a single axis or all the axes as
before.</p>
</dd>
<dt><strong>weights</strong><span class="classifier">array_like, optional</span></dt><dd><p>An array of weights associated with the values in <em class="xref py py-obj">a</em>. Each value in
<em class="xref py py-obj">a</em> contributes to the average according to its associated weight.
The array of weights must be the same shape as <em class="xref py py-obj">a</em> if no axis is
specified, otherwise the weights must have dimensions and shape
consistent with <em class="xref py py-obj">a</em> along the specified axis.
If <em class="xref py py-obj">weights=None</em>, then all data in <em class="xref py py-obj">a</em> are assumed to have a
weight equal to one.
The calculation is:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">avg</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">a</span> <span class="o">*</span> <span class="n">weights</span><span class="p">)</span> <span class="o">/</span> <span class="nb">sum</span><span class="p">(</span><span class="n">weights</span><span class="p">)</span>
</pre></div>
</div>
<p>where the sum is over all included elements.
The only constraint on the values of <em class="xref py py-obj">weights</em> is that <em class="xref py py-obj">sum(weights)</em>
must not be 0.</p>
</dd>
<dt><strong>returned</strong><span class="classifier">bool, optional</span></dt><dd><p>Default is <em class="xref py py-obj">False</em>. If <em class="xref py py-obj">True</em>, the tuple (<a class="reference internal" href="#numpy.average" title="numpy.average"><code class="xref py py-obj docutils literal notranslate"><span class="pre">average</span></code></a>, <em class="xref py py-obj">sum_of_weights</em>)
is returned, otherwise only the average is returned.
If <em class="xref py py-obj">weights=None</em>, <em class="xref py py-obj">sum_of_weights</em> is equivalent to the number of
elements over which the average is taken.</p>
</dd>
<dt><strong>keepdims</strong><span class="classifier">bool, optional</span></dt><dd><p>If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original <em class="xref py py-obj">a</em>.
<em>Note:</em> <em class="xref py py-obj">keepdims</em> will not work with instances of <a class="reference internal" href="numpy.matrix.html#numpy.matrix" title="numpy.matrix"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.matrix</span></code></a>
or other classes whose methods do not support <em class="xref py py-obj">keepdims</em>.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 1.23.0.</span></p>
</div>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>retval, [sum_of_weights]</strong><span class="classifier">array_type or double</span></dt><dd><p>Return the average along the specified axis. When <em class="xref py py-obj">returned</em> is <em class="xref py py-obj">True</em>,
return a tuple with the average as the first element and the sum
of the weights as the second element. <em class="xref py py-obj">sum_of_weights</em> is of the
same type as <em class="xref py py-obj">retval</em>. The result dtype follows a general pattern.
If <em class="xref py py-obj">weights</em> is None, the result dtype will be that of <em class="xref py py-obj">a</em> , or <code class="docutils literal notranslate"><span class="pre">float64</span></code>
if <em class="xref py py-obj">a</em> is integral. Otherwise, if <em class="xref py py-obj">weights</em> is not None and <em class="xref py py-obj">a</em> is non-
integral, the result type will be the type of lowest precision capable of
representing values of both <em class="xref py py-obj">a</em> and <em class="xref py py-obj">weights</em>. If <em class="xref py py-obj">a</em> happens to be
integral, the previous rules still applies but the result dtype will
at least be <code class="docutils literal notranslate"><span class="pre">float64</span></code>.</p>
</dd>
</dl>
</dd>
<dt class="field-odd">Raises<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt>ZeroDivisionError</dt><dd><p>When all weights along axis are zero. See <a class="reference internal" href="numpy.ma.average.html#numpy.ma.average" title="numpy.ma.average"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.ma.average</span></code></a> for a
version robust to this type of error.</p>
</dd>
<dt>TypeError</dt><dd><p>When <em class="xref py py-obj">weights</em> does not have the same shape as <em class="xref py py-obj">a</em>, and <em class="xref py py-obj">axis=None</em>.</p>
</dd>
<dt>ValueError</dt><dd><p>When <em class="xref py py-obj">weights</em> does not have dimensions and shape consistent with <em class="xref py py-obj">a</em>
along specified <em class="xref py py-obj">axis</em>.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="numpy.mean.html#numpy.mean" title="numpy.mean"><code class="xref py py-obj docutils literal notranslate"><span class="pre">mean</span></code></a></dt><dd></dd>
<dt><a class="reference internal" href="numpy.ma.average.html#numpy.ma.average" title="numpy.ma.average"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ma.average</span></code></a></dt><dd><p>average for masked arrays – useful if your data contains “missing” values</p>
</dd>
<dt><a class="reference internal" href="numpy.result_type.html#numpy.result_type" title="numpy.result_type"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.result_type</span></code></a></dt><dd><p>Returns the type that results from applying the numpy type promotion rules to the arguments.</p>
</dd>
</dl>
</div>
<p class="rubric">Examples</p>
<div class="try_examples_outer_container docutils container" id="ee4be604-6c31-4989-8668-f0f342fd6c4a">
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<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="gp">>>> </span><span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">data</span>
<span class="go">array([1, 2, 3, 4])</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">average</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="go">2.5</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">average</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">11</span><span class="p">),</span> <span class="n">weights</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">))</span>
<span class="go">4.0</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">6</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">data</span>
<span class="go">array([[0, 1],</span>
<span class="go"> [2, 3],</span>
<span class="go"> [4, 5]])</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">average</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">weights</span><span class="o">=</span><span class="p">[</span><span class="mf">1.</span><span class="o">/</span><span class="mi">4</span><span class="p">,</span> <span class="mf">3.</span><span class="o">/</span><span class="mi">4</span><span class="p">])</span>
<span class="go">array([0.75, 2.75, 4.75])</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">average</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">weights</span><span class="o">=</span><span class="p">[</span><span class="mf">1.</span><span class="o">/</span><span class="mi">4</span><span class="p">,</span> <span class="mf">3.</span><span class="o">/</span><span class="mi">4</span><span class="p">])</span>
<span class="gt">Traceback (most recent call last):</span>
<span class="w"> </span><span class="o">...</span>
<span class="gr">TypeError</span>: <span class="n">Axis must be specified when shapes of a and weights differ.</span>
</pre></div>
</div>
<p>With <code class="docutils literal notranslate"><span class="pre">keepdims=True</span></code>, the following result has shape (3, 1).</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">average</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="go">array([[0.5],</span>
<span class="go"> [2.5],</span>
<span class="go"> [4.5]])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">8</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">data</span>
<span class="go">array([[[0, 1],</span>
<span class="go"> [2, 3]],</span>
<span class="go"> [[4, 5],</span>
<span class="go"> [6, 7]]])</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">average</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">weights</span><span class="o">=</span><span class="p">[[</span><span class="mf">1.</span><span class="o">/</span><span class="mi">4</span><span class="p">,</span> <span class="mf">3.</span><span class="o">/</span><span class="mi">4</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="o">/</span><span class="mi">2</span><span class="p">]])</span>
<span class="go">array([3.4, 4.4])</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">average</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">weights</span><span class="o">=</span><span class="p">[[</span><span class="mf">1.</span><span class="o">/</span><span class="mi">4</span><span class="p">,</span> <span class="mf">3.</span><span class="o">/</span><span class="mi">4</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="o">/</span><span class="mi">2</span><span class="p">]])</span>
<span class="gt">Traceback (most recent call last):</span>
<span class="w"> </span><span class="o">...</span>
<span class="gr">ValueError</span>: <span class="n">Shape of weights must be consistent</span>
<span class="x">with shape of a along specified axis.</span>
</pre></div>
</div>
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