<h3 dir="auto">Describe the issue:</h3>
<p dir="auto">I have an array of float numbers. Numpy fails to calculate the standard deviation while the manual calculation is okay. There is no <code class="notranslate">nan</code> or <code class="notranslate">inf</code> in the array.</p>
<p dir="auto">If default parameters (<code class="notranslate">ddof=0</code>) are used, no warning is shown, but the warning appears if <code class="notranslate">ddof=1</code> is used.</p>
<p dir="auto">The array can be downloaded from <a href="https://mega.nz/file/2tRjnDjS#KbNGeau3uG1vBRWiW6SyVYzT9gXwVQpDycYzSfgagsk" rel="nofollow">here</a>.</p>
<h3 dir="auto">Reproduce the code example:</h3>
<div class="highlight highlight-source-python notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="np.std(arr, ddof=1)"><pre class="notranslate"><span class="pl-s1">np</span>.<span class="pl-en">std</span>(<span class="pl-s1">arr</span>, <span class="pl-s1">ddof</span><span class="pl-c1">=</span><span class="pl-c1">1</span>)</pre></div>
<h3 dir="auto">Error message:</h3>
<div class="highlight highlight-source-shell notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Actually, it is a warning:


C:\Users\***\miniconda3\envs\py38\lib\site-packages\numpy\core\_methods.py:212: RuntimeWarning: overflow encountered in reduce
  arrmean = umr_sum(arr, axis, dtype, keepdims=True, where=where)"><pre class="notranslate">Actually, it is a warning:


C:<span class="pl-cce">\U</span>sers<span class="pl-cce">\*</span><span class="pl-k">**</span><span class="pl-cce">\m</span>iniconda3<span class="pl-cce">\e</span>nvs<span class="pl-cce">\p</span>y38<span class="pl-cce">\l</span>ib<span class="pl-cce">\s</span>ite-packages<span class="pl-cce">\n</span>umpy<span class="pl-cce">\c</span>ore<span class="pl-cce">\_</span>methods.py:212: RuntimeWarning: overflow encountered <span class="pl-k">in</span> reduce
  arrmean = umr_sum(arr, axis, dtype, keepdims=True, where=where)</pre></div>
<div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="

### NumPy/Python version information:

numpy&gt;=1.22.4
Python==3.8.13

### Context for the issue:

_No response_"><pre class="notranslate"><code class="notranslate">

### NumPy/Python version information:

numpy&gt;=1.22.4
Python==3.8.13

### Context for the issue:

_No response_
</code></pre></div>
<p dir="auto"><a class="issue-link js-issue-link" data-error-text="Failed to load title" data-id="186048633" data-permission-text="Title is private" data-url="https://github.com/numpy/numpy/issues/8222" data-hovercard-type="pull_request" data-hovercard-url="/numpy/numpy/pull/8222/hovercard" href="https://github.com/numpy/numpy/pull/8222">#8222</a> raised the numerical precision in float16 of numpy.mean.</p>
<p dir="auto">As per comment <a class="issue-link js-issue-link" data-error-text="Failed to load title" data-id="186048633" data-permission-text="Title is private" data-url="https://github.com/numpy/numpy/issues/8222" data-hovercard-type="pull_request" data-hovercard-url="/numpy/numpy/pull/8222/hovercard?comment_id=257406456&amp;comment_type=issue_comment" href="https://github.com/numpy/numpy/pull/8222#issuecomment-257406456">#8222 (comment)</a>, this can also be done for numpy.std and numpy.var</p>
<hr>
Summary 2019-04-26 by <a class="user-mention notranslate" data-hovercard-type="user" data-hovercard-url="/users/stefanv/hovercard" data-octo-click="hovercard-link-click" data-octo-dimensions="link_type:self" href="https://github.com/stefanv">@stefanv</a>:
<ul dir="auto">
<li>Float16 operations are implemented in software; as such intermediate computations can be done in float32 without loss of speed</li>
<li>For <code class="notranslate">numpy.mean</code>, the intermediary type is modified <a href="https://github.com/numpy/numpy/blob/maintenance/1.16.x/numpy/core/_methods.py#L71">here</a>.</li>
<li>A similar change can be made in the same file for <code class="notranslate">_var</code> and <code class="notranslate">_std</code></li>
</ul>