https://mathresearch.utsa.edu/wiki/index.php?action=history&feed=atom&title=Standard_Deviation Standard Deviation - Revision history 2026-06-09T06:19:51Z Revision history for this page on the wiki MediaWiki 1.34.1 https://mathresearch.utsa.edu/wiki/index.php?title=Standard_Deviation&diff=3287&oldid=prev Khanh at 16:42, 30 October 2021 2021-10-30T16:42:42Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 16:42, 30 October 2021</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l322" >Line 322:</td> <td colspan="2" class="diff-lineno">Line 322:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [https://www.youtube.com/watch?v=IaTFpp-uzp0 How To Calculate The Standard Deviation], The Organic Chemistry Tutor</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [https://www.youtube.com/watch?v=IaTFpp-uzp0 How To Calculate The Standard Deviation], The Organic Chemistry Tutor</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [https://www.youtube.com/watch?v=Uk98hiMQgN0 Standard Deviation Formula, Statistics, Variance, Sample and Population Mean], The Organic Chemistry Tutor</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [https://www.youtube.com/watch?v=Uk98hiMQgN0 Standard Deviation Formula, Statistics, Variance, Sample and Population Mean], The Organic Chemistry Tutor</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">==References==</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># Bland, J.M.; Altman, D.G. (1996). &quot;Statistics notes: measurement error&quot;. BMJ. 312 (7047): 1654. doi:10.1136/bmj.312.7047.1654. PMC 2351401. PMID 8664723.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># &quot;List of Probability and Statistics Symbols&quot;. Math Vault. 26 April 2020. Retrieved 21 August 2020.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># Gauss, Carl Friedrich (1816). &quot;Bestimmung der Genauigkeit der Beobachtungen&quot;. Zeitschrift für Astronomie und Verwandte Wissenschaften. 1: 187–197.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># Walker, Helen (1931). Studies in the History of the Statistical Method. Baltimore, MD: Williams &amp; Wilkins Co. pp. 24–25.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># Weisstein, Eric W. &quot;Bessel's Correction&quot;. MathWorld.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># &quot;Standard Deviation Formulas&quot;. www.mathsisfun.com. Retrieved 21 August 2020.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># Weisstein, Eric W. &quot;Standard Deviation&quot;. mathworld.wolfram.com. Retrieved 21 August 2020.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># Gurland, John; Tripathi, Ram C. (1971), &quot;A Simple Approximation for Unbiased Estimation of the Standard Deviation&quot;, The American Statistician, 25 (4): 30–32, doi:10.2307/2682923, JSTOR 2682923</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># &quot;Standard Deviation Calculator&quot;. PureCalculators. 11 July 2021. Retrieved 14 September 2021.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># Shiffler, Ronald E.; Harsha, Phillip D. (1980). &quot;Upper and Lower Bounds for the Sample Standard Deviation&quot;. Teaching Statistics. 2 (3): 84–86. doi:10.1111/j.1467-9639.1980.tb00398.x.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># Browne, Richard H. (2001). &quot;Using the Sample Range as a Basis for Calculating Sample Size in Power Calculations&quot;. The American Statistician. 55 (4): 293–298. doi:10.1198/000313001753272420. JSTOR 2685690. S2CID 122328846.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># &quot;CERN experiments observe particle consistent with long-sought Higgs boson | CERN press office&quot;. Press.web.cern.ch. 4 July 2012. Retrieved 30 May 2015.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># LIGO Scientific Collaboration, Virgo Collaboration (2016), &quot;Observation of Gravitational Waves from a Binary Black Hole Merger&quot;, Physical Review Letters, 116 (6): 061102, arXiv:1602.03837, Bibcode:2016PhRvL.116f1102A, doi:10.1103/PhysRevLett.116.061102, PMID 26918975, S2CID 124959784</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># Alister Doyle (25 February 2019). &quot;Evidence for man-made global warming hits 'gold standard': scientists&quot;. Reuters. Retrieved 23 March 2021.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># &quot;What is Standard Deviation&quot;. Pristine. Retrieved 29 October 2011.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># Ghahramani, Saeed (2000). Fundamentals of Probability (2nd ed.). New Jersey: Prentice Hall. p. 438.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># Eric W. Weisstein. &quot;Distribution Function&quot;. MathWorld—A Wolfram Web Resource. Retrieved 30 September 2014.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># Welford, BP (August 1962). &quot;Note on a Method for Calculating Corrected Sums of Squares and Products&quot;. Technometrics. 4 (3): 419–420. CiteSeerX 10.1.1.302.7503. doi:10.1080/00401706.1962.10490022.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># Dodge, Yadolah (2003). The Oxford Dictionary of Statistical Terms. Oxford University Press. ISBN 978-0-19-920613-1.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># Pearson, Karl (1894). &quot;On the dissection of asymmetrical frequency curves&quot;. Philosophical Transactions of the Royal Society A. 185: 71–110. Bibcode:1894RSPTA.185...71P. doi:10.1098/rsta.1894.0003.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># Miller, Jeff. &quot;Earliest Known Uses of Some of the Words of Mathematics&quot;</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Licensing ==  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Licensing ==  </div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Content obtained and/or adapted from:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Content obtained and/or adapted from:</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [https://en.wikipedia.org/wiki/Standard_deviation Standard deviation, Wikipedia] under a CC BY-SA license</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [https://en.wikipedia.org/wiki/Standard_deviation Standard deviation, Wikipedia] under a CC BY-SA license</div></td></tr> </table> Khanh https://mathresearch.utsa.edu/wiki/index.php?title=Standard_Deviation&diff=2881&oldid=prev Khanh at 17:31, 24 October 2021 2021-10-24T17:31:43Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 17:31, 24 October 2021</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l345" >Line 345:</td> <td colspan="2" class="diff-lineno">Line 345:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Pearson, Karl (1894). &quot;On the dissection of asymmetrical frequency curves&quot;. Philosophical Transactions of the Royal Society A. 185: 71–110. Bibcode:1894RSPTA.185...71P. doi:10.1098/rsta.1894.0003.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Pearson, Karl (1894). &quot;On the dissection of asymmetrical frequency curves&quot;. Philosophical Transactions of the Royal Society A. 185: 71–110. Bibcode:1894RSPTA.185...71P. doi:10.1098/rsta.1894.0003.</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Miller, Jeff. &quot;Earliest Known Uses of Some of the Words of Mathematics&quot;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Miller, Jeff. &quot;Earliest Known Uses of Some of the Words of Mathematics&quot;</div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">== Licensing == </ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Content obtained and/or adapted from:</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* [https://en.wikipedia.org/wiki/Standard_deviation Standard deviation, Wikipedia] under a CC BY-SA license</ins></div></td></tr> </table> Khanh https://mathresearch.utsa.edu/wiki/index.php?title=Standard_Deviation&diff=1713&oldid=prev Khanh at 23:03, 2 October 2021 2021-10-02T23:03:07Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 23:03, 2 October 2021</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l43" >Line 43:</td> <td colspan="2" class="diff-lineno">Line 43:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Standard deviation of average height for adult men===</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Standard deviation of average height for adult men===</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>If the population of interest is approximately normally distributed, the standard deviation provides information on the proportion of observations above or below certain values. For example, the average height for adult men in the United States is about 70&amp;nbsp;inches (177.8&amp;nbsp;cm), with a standard deviation of around 3&amp;nbsp;inches (7.62&amp;nbsp;cm). This means that most men (about 68%, assuming a normal distribution) have a height within 3&amp;nbsp;inches (7.62&amp;nbsp;cm) of the mean (67–73&amp;nbsp;inches (170.18–185.42&amp;nbsp;cm)) - one standard deviation - and almost all men (about 95%) have a height within 6&amp;nbsp;inches (15.24&amp;nbsp;cm) of the mean (64–76&amp;nbsp;inches (162.56–193.04&amp;nbsp;cm))- two standard deviations. If the standard deviation were zero, then all men would be exactly 70&amp;nbsp;inches (177.8&amp;nbsp;cm) tall. If the standard deviation were 20&amp;nbsp;inches (50.8&amp;nbsp;cm), then men would have much more variable heights, with a typical range of about 50–90&amp;nbsp;inches (127–228.6&amp;nbsp;cm). Three standard deviations account for 99.7% of the sample population being studied, assuming the distribution is normal or bell-shaped (see the 68-95-99.7 rule, or the ''empirical rule,'' for more information).</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>If the population of interest is approximately normally distributed, the standard deviation provides information on the proportion of observations above or below certain values. For example, the average height for adult men in the United States is about 70&amp;nbsp;inches (177.8&amp;nbsp;cm), with a standard deviation of around 3&amp;nbsp;inches (7.62&amp;nbsp;cm). This means that most men (about 68%, assuming a normal distribution) have a height within 3&amp;nbsp;inches (7.62&amp;nbsp;cm) of the mean (67–73&amp;nbsp;inches (170.18–185.42&amp;nbsp;cm)) - one standard deviation - and almost all men (about 95%) have a height within 6&amp;nbsp;inches (15.24&amp;nbsp;cm) of the mean (64–76&amp;nbsp;inches (162.56–193.04&amp;nbsp;cm)) - two standard deviations. If the standard deviation were zero, then all men would be exactly 70&amp;nbsp;inches (177.8&amp;nbsp;cm) tall. If the standard deviation were 20&amp;nbsp;inches (50.8&amp;nbsp;cm), then men would have much more variable heights, with a typical range of about 50–90&amp;nbsp;inches (127–228.6&amp;nbsp;cm). Three standard deviations account for 99.7% of the sample population being studied, assuming the distribution is normal or bell-shaped (see the 68-95-99.7 rule, or the ''empirical rule,'' for more information).</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Definition of population values==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Definition of population values==</div></td></tr> </table> Khanh https://mathresearch.utsa.edu/wiki/index.php?title=Standard_Deviation&diff=1712&oldid=prev Khanh at 23:02, 2 October 2021 2021-10-02T23:02:12Z <p></p> <a href="https://mathresearch.utsa.edu/wiki/index.php?title=Standard_Deviation&amp;diff=1712&amp;oldid=1528">Show changes</a> Khanh https://mathresearch.utsa.edu/wiki/index.php?title=Standard_Deviation&diff=1528&oldid=prev Khanh: Created page with "* [https://www.youtube.com/watch?v=IaTFpp-uzp0 How To Calculate The Standard Deviation], The Organic Chemistry Tutor * [https://www.youtube.com/watch?v=Uk98hiMQgN0 Standard De..." 2021-09-27T03:14:59Z <p>Created page with &quot;* [https://www.youtube.com/watch?v=IaTFpp-uzp0 How To Calculate The Standard Deviation], The Organic Chemistry Tutor * [https://www.youtube.com/watch?v=Uk98hiMQgN0 Standard De...&quot;</p> <p><b>New page</b></p><div>* [https://www.youtube.com/watch?v=IaTFpp-uzp0 How To Calculate The Standard Deviation], The Organic Chemistry Tutor<br /> * [https://www.youtube.com/watch?v=Uk98hiMQgN0 Standard Deviation Formula, Statistics, Variance, Sample and Population Mean], The Organic Chemistry Tutor</div> Khanh