https://wikimd.org/index.php?action=history&feed=atom&title=Index_of_dispersion Index of dispersion - Revision history 2026-04-26T23:07:05Z Revision history for this page on the wiki MediaWiki 1.44.2 https://wikimd.org/index.php?title=Index_of_dispersion&diff=6528693&oldid=prev Prab at 17:28, 18 March 2025 2025-03-18T17:28:49Z <p></p> <table style="background-color: #fff; color: #202122;" 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: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 17:28, 18 March 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l32">Line 32:</td> <td colspan="2" class="diff-lineno">Line 32:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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>{{Statistics-stub}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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>{{Statistics-stub}}</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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>{{No image}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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>{{No image}}</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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;">__NOINDEX__</del></div></td><td colspan="2" class="diff-side-added"></td></tr> </table> Prab https://wikimd.org/index.php?title=Index_of_dispersion&diff=6509802&oldid=prev Prab: CSV import 2025-03-17T14:47:01Z <p>CSV import</p> <table style="background-color: #fff; color: #202122;" 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: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:47, 17 March 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l32">Line 32:</td> <td colspan="2" class="diff-lineno">Line 32:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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>{{Statistics-stub}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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>{{Statistics-stub}}</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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>{{No image}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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>{{No image}}</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;">__NOINDEX__</ins></div></td></tr> </table> Prab https://wikimd.org/index.php?title=Index_of_dispersion&diff=6269562&oldid=prev Prab: CSV import 2025-02-11T01:55:10Z <p>CSV import</p> <table style="background-color: #fff; color: #202122;" 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: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 01:55, 11 February 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l31">Line 31:</td> <td colspan="2" class="diff-lineno">Line 31:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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>{{Statistics-stub}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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>{{Statistics-stub}}</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;">{{No image}}</ins></div></td></tr> </table> Prab https://wikimd.org/index.php?title=Index_of_dispersion&diff=5412720&oldid=prev Prab: CSV import 2024-03-19T10:36:19Z <p>CSV import</p> <p><b>New page</b></p><div>&#039;&#039;&#039;Index of Dispersion&#039;&#039;&#039;<br /> <br /> The &#039;&#039;&#039;Index of Dispersion&#039;&#039;&#039;, also known as the &#039;&#039;&#039;dispersion index&#039;&#039;&#039;, &#039;&#039;&#039;coefficient of dispersion&#039;&#039;&#039;, or &#039;&#039;&#039;relative variance&#039;&#039;&#039;, is a measure used in [[statistics]] to quantify how spread out the values of a dataset are, relative to the mean of the dataset. It is defined as the ratio of the [[variance]] to the [[mean]]. This statistical measure is particularly useful in identifying whether a dataset follows a [[Poisson distribution]], where the index of dispersion equals 1, indicating a random distribution. Values greater than 1 suggest over-dispersion, while values less than 1 indicate under-dispersion relative to a Poisson model.<br /> <br /> ==Definition==<br /> The index of dispersion is calculated using the formula:<br /> <br /> \[D = \frac{\sigma^2}{\mu}\]<br /> <br /> where \(D\) is the index of dispersion, \(\sigma^2\) is the variance of the dataset, and \(\mu\) is the mean of the dataset.<br /> <br /> ==Applications==<br /> The index of dispersion is widely used in various fields such as [[ecology]], where it helps in understanding the spatial distribution of species, in [[quality control]] to assess the variability of manufacturing processes, and in [[health sciences]] for analyzing the distribution of disease incidents. It is also applied in [[finance]] to measure the volatility of asset returns relative to their average.<br /> <br /> ==Interpretation==<br /> - **D = 1**: The data is randomly distributed, following a Poisson distribution.<br /> - **D &gt; 1**: Indicates over-dispersion; the data are more spread out than a Poisson distribution would suggest. This might be due to the presence of outliers, clustering, or heterogeneity in the data.<br /> - **D &lt; 1**: Suggests under-dispersion; the data are less spread out than expected in a Poisson distribution. This could be due to negative correlation among data points or uniformity.<br /> <br /> ==See Also==<br /> * [[Variance]]<br /> * [[Mean]]<br /> * [[Poisson distribution]]<br /> * [[Statistical dispersion]]<br /> <br /> ==References==<br /> &lt;references/&gt;<br /> <br /> [[Category:Statistical ratios]]<br /> [[Category:Summary statistics]]<br /> <br /> {{Statistics-stub}}</div> Prab