<commit_before><!--

@license Apache-2.0

Copyright (c) 2020 The Stdlib Authors.

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

   http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.

-->

# snanstdevch

> Calculate the [standard deviation][standard-deviation] of a single-precision floating-point strided array ignoring `NaN` values and using a one-pass trial mean algorithm.

<section class="intro">

The population [standard deviation][standard-deviation] of a finite size population of size `N` is given by

<!-- <equation class="equation" label="eq:population_standard_deviation" align="center" raw="\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}" alt="Equation for the population standard deviation."> -->

<div class="equation" align="center" data-raw-text="\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}" data-equation="eq:population_standard_deviation">
    <img src="" alt="Equation for the population standard deviation.">
    <br>
</div>

<!-- </equation> -->

where the population mean is given by

<!-- <equation class="equation" label="eq:population_mean" align="center" raw="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" alt="Equation for the population mean."> -->

<div class="equation" align="center" data-raw-text="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" data-equation="eq:population_mean">
    <img src="" alt="Equation for the population mean.">
    <br>
</div>

<!-- </equation> -->

Often in the analysis of data, the true population [standard deviation][standard-deviation] is not known _a priori_ and must be estimated from a sample drawn from the population distribution. If one attempts to use the formula for the population [standard deviation][standard-deviation], the result is biased and yields an **uncorrected sample standard deviation**. To compute a **corrected sample standard deviation** for a sample of size `n`,

<!-- <equation class="equation" label="eq:corrected_sample_standard_deviation" align="center" raw="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}" alt="Equation for computing a corrected sample standard deviation."> -->

<div class="equation" align="center" data-raw-text="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}" data-equation="eq:corrected_sample_standard_deviation">
    <img src="" alt="Equation for computing a corrected sample standard deviation.">
    <br>
</div>

<!-- </equation> -->

where the sample mean is given by

<!-- <equation class="equation" label="eq:sample_mean" align="center" raw="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the sample mean."> -->

<div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:sample_mean">
    <img src="" alt="Equation for the sample mean.">
    <br>
</div>

<!-- </equation> -->

The use of the term `n-1` is commonly referred to as Bessel's correction. Note, however, that applying Bessel's correction can increase the mean squared error between the sample standard deviation and population standard deviation. Depending on the characteristics of the population distribution, other correction factors (e.g., `n-1.5`, `n+1`, etc) can yield better estimators.<commit_msg>Update equation src URLs<commit_after><!--

@license Apache-2.0

Copyright (c) 2020 The Stdlib Authors.

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

   http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.

-->

# snanstdevch

> Calculate the [standard deviation][standard-deviation] of a single-precision floating-point strided array ignoring `NaN` values and using a one-pass trial mean algorithm.

<section class="intro">

The population [standard deviation][standard-deviation] of a finite size population of size `N` is given by

<!-- <equation class="equation" label="eq:population_standard_deviation" align="center" raw="\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}" alt="Equation for the population standard deviation."> -->

<div class="equation" align="center" data-raw-text="\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}" data-equation="eq:population_standard_deviation">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/7dd4b789ac30ef94a4ae9b162ee6ae5a5b28b41a/lib/node_modules/@stdlib/stats/base/snanstdevch/docs/img/equation_population_standard_deviation.svg" alt="Equation for the population standard deviation.">
    <br>
</div>

<!-- </equation> -->

where the population mean is given by

<!-- <equation class="equation" label="eq:population_mean" align="center" raw="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" alt="Equation for the population mean."> -->

<div class="equation" align="center" data-raw-text="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" data-equation="eq:population_mean">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/7dd4b789ac30ef94a4ae9b162ee6ae5a5b28b41a/lib/node_modules/@stdlib/stats/base/snanstdevch/docs/img/equation_population_mean.svg" alt="Equation for the population mean.">
    <br>
</div>

<!-- </equation> -->

Often in the analysis of data, the true population [standard deviation][standard-deviation] is not known _a priori_ and must be estimated from a sample drawn from the population distribution. If one attempts to use the formula for the population [standard deviation][standard-deviation], the result is biased and yields an **uncorrected sample standard deviation**. To compute a **corrected sample standard deviation** for a sample of size `n`,

<!-- <equation class="equation" label="eq:corrected_sample_standard_deviation" align="center" raw="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}" alt="Equation for computing a corrected sample standard deviation."> -->

<div class="equation" align="center" data-raw-text="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}" data-equation="eq:corrected_sample_standard_deviation">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/7dd4b789ac30ef94a4ae9b162ee6ae5a5b28b41a/lib/node_modules/@stdlib/stats/base/snanstdevch/docs/img/equation_corrected_sample_standard_deviation.svg" alt="Equation for computing a corrected sample standard deviation.">
    <br>
</div>

<!-- </equation> -->

where the sample mean is given by

<!-- <equation class="equation" label="eq:sample_mean" align="center" raw="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the sample mean."> -->

<div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:sample_mean">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/7dd4b789ac30ef94a4ae9b162ee6ae5a5b28b41a/lib/node_modules/@stdlib/stats/base/snanstdevch/docs/img/equation_sample_mean.svg" alt="Equation for the sample mean.">
    <br>
</div>

<!-- </equation> -->

The use of the term `n-1` is commonly referred to as Bessel's correction. Note, however, that applying Bessel's correction can increase the mean squared error between the sample standard deviation and population standard deviation. Depending on the characteristics of the population distribution, other correction factors (e.g., `n-1.5`, `n+1`, etc) can yield better estimators.
{'fraction_non_alphanumeric': 0.14754304386075154, 'fraction_numerical': 0.021616187005152696, 'mean_word_length': 5.0105740181268885, 'pattern_counts': {'":': 0, '<': 71, '<?xml version=': 0, '>': 73, 'https://': 4, 'lorem ipsum': 0, 'www.': 2, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
{'dir': 'git-commits-cleaned', 'id': '824850', 'n_tokens_mistral': 2596, 'n_tokens_neox': 2424, 'n_words': 786}