{"id":779,"date":"2020-02-13T07:44:09","date_gmt":"2020-02-13T07:44:09","guid":{"rendered":"https:\/\/bcisnotes.com\/thirdsemester\/?p=779"},"modified":"2020-02-16T08:48:37","modified_gmt":"2020-02-16T08:48:37","slug":"range-quartile-deviation-and-standard-deviation-measures-of-dispersion-bcis-notes","status":"publish","type":"post","link":"https:\/\/bcisnotes.com\/thirdsemester\/business-statistics\/range-quartile-deviation-and-standard-deviation-measures-of-dispersion-bcis-notes\/","title":{"rendered":"Range, Quartile Deviation, and Standard Deviation || Measures of Dispersion || Bcis Notes"},"content":{"rendered":"<h2>Range, Quartile Deviation, and Standard Deviation<\/h2>\n<h2>1. Range<\/h2>\n<p>The Range is defined as the difference between the largest item and the smallest item in a set of observations. If L = Largest item and S = Smallest item and their range are denoted by &#8216;R&#8217; and given by:<\/p>\n<p>R = L &#8211; S<\/p>\n<h3>Coefficient of Range<\/h3>\n<p>The range is of absolute measure. The relative measures corresponding to the range is known as the coefficient of range and is given by:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-786\" src=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_125737-300x35.png\" alt=\"Coefficient of Range\" width=\"300\" height=\"35\" srcset=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_125737-300x35.png 300w, https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_125737.png 500w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>&nbsp;<\/p>\n<h2>2. Quartile Deviation or Semi-interquartile range<\/h2>\n<p>The measures of dispersion based on upper quartile and lower quartile is called quartile deviation.<\/p>\n<p>The difference between the upper quartile and lower quartile is called the inter-quartile range.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-790\" src=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_130122-300x17.png\" alt=\"Inter-quartile Range\" width=\"300\" height=\"17\" srcset=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_130122-300x17.png 300w, https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_130122-768x44.png 768w, https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_130122.png 934w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Half of the inter-quartile range is called the quartile deviation.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-801\" src=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_130818-300x40.png\" alt=\"Quartile Deviation \" width=\"300\" height=\"40\" srcset=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_130818-300x40.png 300w, https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_130818-768x103.png 768w, https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_130818.png 928w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>&nbsp;<\/p>\n<h3>Coefficient of Quartile Deviation<\/h3>\n<p>The relative measure of dispersion based on the upper quartile and lower quartile is called the coefficient of quartile deviation.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-800\" src=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_130648-300x28.png\" alt=\"Coefficient of Quartile Deviation \" width=\"300\" height=\"28\" srcset=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_130648-300x28.png 300w, https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_130648-1024x96.png 1024w, https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_130648-768x72.png 768w, https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_130648-1536x144.png 1536w, https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_130648-2048x192.png 2048w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<h2>3. Standard Deviation<\/h2>\n<p>It is defined as a positive square root of the mean of the square of deviation of items taken from their arithmetic. It is denoted by:<\/p>\n<h4><span style=\"text-decoration: underline;\">Individual Series<\/span><\/h4>\n<h5>Direct Method<\/h5>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-807\" src=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_131346-300x47.png\" alt=\"Direct Method\" width=\"300\" height=\"47\" srcset=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_131346-300x47.png 300w, https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_131346.png 565w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<h5>Shortcut Method<\/h5>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-810\" src=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_131538-300x68.png\" alt=\"Shortcut Method\" width=\"300\" height=\"68\" srcset=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_131538-300x68.png 300w, https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_131538.png 305w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>where,<\/p>\n<p>d = X &#8211; a<\/p>\n<p>a = Assumed Mean<\/p>\n<h4><span style=\"text-decoration: underline;\">Discrete Series<\/span><\/h4>\n<h5>Direct Method<\/h5>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-816\" src=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_133400-300x44.png\" alt=\"Direct Method,\" width=\"300\" height=\"44\" srcset=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_133400-300x44.png 300w, https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_12022020_133400.png 600w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<h5>Shortcut Method<\/h5>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-825\" src=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_13022020_124611-300x61.png\" alt=\"Shortcut Method\" width=\"300\" height=\"61\" srcset=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_13022020_124611-300x61.png 300w, https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_13022020_124611.png 340w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<h4><span style=\"text-decoration: underline;\">Continuous Series<\/span><\/h4>\n<h5>Step-deviation Method<\/h5>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-829\" src=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_13022020_125030-300x50.png\" alt=\"Step-deviation Method\" width=\"300\" height=\"50\" srcset=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_13022020_125030-300x50.png 300w, https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_13022020_125030.png 410w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<h3>Coefficient of Standard Deviation<\/h3>\n<p>The relative measures of dispersion based on the standard deviation is called the coefficient of standard deviation.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-830\" src=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_13022020_125312-300x42.png\" alt=\"Coefficient of Standard Deviation\" width=\"300\" height=\"42\" srcset=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_13022020_125312-300x42.png 300w, https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_13022020_125312.png 412w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<h3>Property of Standard Deviation<\/h3>\n<ol>\n<li>Standard Deviation is independent of the change of origin but not of the scale.<\/li>\n<\/ol>\n<p>Change of origin = (+\/-)<\/p>\n<p>Change of scale= <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-832\" src=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_13022020_125830.png\" alt=\"Change of scale\" width=\"69\" height=\"20\" \/><\/p>\n<p>2. Let n1 and n2 be the sizes and\u00a0 \u00a0be the mean and \u03c31 and \u03c32 be the Standard Deviation of two series and their combined\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Standard Deviation is denoted by:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-833\" src=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_13022020_130500-300x55.png\" alt=\"Property of Standard Deviation\" width=\"300\" height=\"55\" srcset=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_13022020_130500-300x55.png 300w, https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_13022020_130500.png 484w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Here,<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-834\" src=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_13022020_130701.png\" alt=\"n1 and n2\" width=\"197\" height=\"22\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-835\" src=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_13022020_130741.png\" alt=\"Here,\" width=\"197\" height=\"22\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-836\" src=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_13022020_131122.png\" alt=\"Deviation\" width=\"296\" height=\"65\" \/><\/p>\n<p>&nbsp;<\/p>\n<h2>4. Variance<\/h2>\n<p>The square of standard deviation is called variance. It is denoted by \u03c3\u00b2 or \u00b5.<\/p>\n<h3>Coefficient of Variance (C.V)<\/h3>\n<p>The relative measure of Standard Deviation is multiplied by 100 is called Coefficient of Variance.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-831\" src=\"https:\/\/bcisnotes.com\/thirdsemester\/wp-content\/uploads\/2020\/02\/vme_img_13022020_125725.png\" alt=\"Coefficient of Variance (C.V)\" width=\"244\" height=\"49\" \/><\/p>\n<p>Two series can be compared with the help of the Coefficient of Variance for their variability. Less the value of Coefficient of Variance more will be consistent or uniform and vice versa.<\/p>\n<p>You may also like:\u00a0<a href=\"https:\/\/bcisnotes.com\/thirdsemester\/business-statistics\/mode-measures-of-central-tendancy-bcis-notes\/\" target=\"_blank\" rel=\"noopener noreferrer\">Mode || Measures of Central Tendency<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<div class=\"mh-excerpt\"><p>Range, Quartile Deviation, and Standard Deviation 1. Range The Range is defined as the difference between the largest item and the smallest item in a <a class=\"mh-excerpt-more\" href=\"https:\/\/bcisnotes.com\/thirdsemester\/business-statistics\/range-quartile-deviation-and-standard-deviation-measures-of-dispersion-bcis-notes\/\" title=\"Range, Quartile Deviation, and Standard Deviation || Measures of Dispersion || Bcis Notes\">[&#8230;]<\/a><\/p>\n<\/div>","protected":false},"author":4,"featured_media":840,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Range, Quartile &amp; Standard Deviation || Dispersion || Bcis Notes<\/title>\n<meta name=\"description\" content=\"Range, Quartile Deviation, and Standard Deviation are three of the must commom measures of the disperion of the data. 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