{"id":517,"date":"2024-04-09T01:17:29","date_gmt":"2024-04-09T05:17:29","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/?post_type=chapter&#038;p=517"},"modified":"2024-04-09T01:50:36","modified_gmt":"2024-04-09T05:50:36","slug":"excel-formulas","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/excel-formulas\/","title":{"raw":"Excel Formulas","rendered":"Excel Formulas"},"content":{"raw":"<div class=\"formulas\">\r\n<p class=\"import-Normal\"><strong><code><\/code><\/strong><\/p>\r\n\r\n<h2 class=\"import-Normal\"><strong>Excel<\/strong> <strong>Commands<\/strong><\/h2>\r\n<table style=\"width: 819px;height: 398px\">\r\n<tbody>\r\n<tr class=\"TableNormal-R\" style=\"height: 18pt\">\r\n<td class=\"TableNormal-C\" style=\"border-width: 0pt 0.5pt 0.5pt 0pt;border-style: none solid solid none;border-color: windowtext #a5a5a5 #a5a5a5 windowtext;padding: 0px 0pt;width: 33.0694px;height: 36px\">\r\n<p class=\"import-TableParagraph\"><\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0pt 0.5pt 0.5pt;border-style: none solid solid;border-color: windowtext #a5a5a5 #a5a5a5;padding: 0px 0pt;width: 80.1667px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.1pt\">A<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0pt 0.5pt 0.5pt;border-style: none solid solid;border-color: windowtext #a5a5a5 #a5a5a5;padding: 0px 0pt;width: 139.292px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.15pt\">B<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0pt 0.5pt 0.5pt;border-style: none solid solid;border-color: windowtext #a5a5a5 #a5a5a5;padding: 0px 0pt;width: 235.5px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">C<\/p>\r\n<\/td>\r\n<td style=\"background-color: #bfbfbf;border-width: 0pt 0.5pt 0.5pt;border-style: none solid solid;border-color: windowtext #a5a5a5 #a5a5a5;padding: 0px 0pt;width: 99.2083px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">D<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0pt 0.5pt 0.5pt;border-style: none solid solid;border-color: windowtext #a5a5a5 #a5a5a5;padding: 0px 0pt;width: 225.542px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">E<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr class=\"TableNormal-R\" style=\"height: 17.95pt\">\r\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0.5pt 0.5pt 0.5pt 0pt;border-style: solid solid solid none;border-color: #a5a5a5 #a5a5a5 #a5a5a5 windowtext;padding: 0px 0pt;width: 33.0694px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"text-align: right;margin-right: 5.6pt\">1<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"background-color: #fffbcc;padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 80.1667px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.1pt\"><strong>X<\/strong><\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"background-color: #fffbcc;padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 139.292px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.15pt\"><strong>Name<\/strong><\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"background-color: #fffbcc;padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 235.5px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\"><strong>Command<\/strong><\/p>\r\n<\/td>\r\n<td style=\"background-color: #fffbcc;padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 99.2083px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\"><strong>Answer<\/strong><\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"background-color: #fffbcc;padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 225.542px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\"><strong>Answer (with Notes)<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr class=\"TableNormal-R\" style=\"height: 17.95pt\">\r\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0.5pt 0.5pt 0.5pt 0pt;border-style: solid solid solid none;border-color: #a5a5a5 #a5a5a5 #a5a5a5 windowtext;padding: 0px 0pt;width: 33.0694px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"text-align: right;margin-right: 5.6pt\">2<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 80.1667px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.1pt\">$20,000<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 139.292px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.15pt\">Range<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 235.5px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">=MAX(A2:A8)-MIN(A2:A8)<\/p>\r\n<\/td>\r\n<td style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 99.2083px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">$25,000<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 225.542px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">Finds the range<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr class=\"TableNormal-R\" style=\"height: 17.95pt\">\r\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0.5pt 0.5pt 0.5pt 0pt;border-style: solid solid solid none;border-color: #a5a5a5 #a5a5a5 #a5a5a5 windowtext;padding: 0px 0pt;width: 33.0694px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"text-align: right;margin-right: 5.6pt\">3<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 80.1667px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.1pt\">$25,000<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 139.292px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.15pt\">Population Standard Deviation<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 235.5px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">=STDEV.P(A2:A8)<\/p>\r\n<\/td>\r\n<td style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 99.2083px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">$8,539.13<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 225.542px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">Finds the population standard deviation<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr class=\"TableNormal-R\" style=\"height: 32.4pt\">\r\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0.5pt 0.5pt 0.5pt 0pt;border-style: solid solid solid none;border-color: #a5a5a5 #a5a5a5 #a5a5a5 windowtext;padding: 0px 0pt;width: 33.0694px;height: 42px\">\r\n<p class=\"import-TableParagraph\" style=\"text-align: right;margin-right: 5.6pt\">4<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 80.1667px;height: 42px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.1pt\">$30,000<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 139.292px;height: 42px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.15pt\">Sample Standard Deviation<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 235.5px;height: 42px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">=STDEV.S(A2:A8)<\/p>\r\n<\/td>\r\n<td style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 99.2083px;height: 42px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt;margin-right: 5.55pt\">$9,354.14<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 225.542px;height: 42px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt;margin-right: 5.55pt\">Finds the sample standard deviation<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr class=\"TableNormal-R\" style=\"height: 32.4pt\">\r\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0.5pt 0.5pt 0.5pt 0pt;border-style: solid solid solid none;border-color: #a5a5a5 #a5a5a5 #a5a5a5 windowtext;padding: 0px 0pt;width: 33.0694px;height: 42px\">\r\n<p class=\"import-TableParagraph\" style=\"text-align: right;margin-right: 5.6pt\">5<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 80.1667px;height: 42px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.1pt\">$35,000<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 139.292px;height: 42px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.15pt\">Population Variance<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 235.5px;height: 42px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">=VAR.P(A2:A8)<\/p>\r\n<\/td>\r\n<td style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 99.2083px;height: 42px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt;margin-right: 5.55pt\">72,916,667<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 225.542px;height: 42px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt;margin-right: 5.55pt\">Finds the population variance<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr class=\"TableNormal-R\" style=\"height: 17.95pt\">\r\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0.5pt 0.5pt 0.5pt 0pt;border-style: solid solid solid none;border-color: #a5a5a5 #a5a5a5 #a5a5a5 windowtext;padding: 0px 0pt;width: 33.0694px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"text-align: right;margin-right: 5.6pt\">6<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 80.1667px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.1pt\">$40,000<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 139.292px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.15pt\">Sample Variance<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 235.5px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">=VAR.S(A2:A8)<\/p>\r\n<\/td>\r\n<td style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 99.2083px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">87,500,000<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 225.542px;height: 36px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">Finds the sample variance<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr class=\"TableNormal-R\" style=\"height: 46.8pt\">\r\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0.5pt 0.5pt 0.5pt 0pt;border-style: solid solid solid none;border-color: #a5a5a5 #a5a5a5 #a5a5a5 windowtext;padding: 0px 0pt;width: 33.0694px;height: 73px\">\r\n<p class=\"import-TableParagraph\" style=\"text-align: right;margin-right: 5.6pt\">7<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 80.1667px;height: 73px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.1pt\">$45,000<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 139.292px;height: 73px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.15pt;margin-right: 6.25pt\">Coefficient of Variation (Population)<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 235.5px;height: 73px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">=VAR.P(A2:A8) \/AVERAGE(A2:A8)<\/p>\r\n<\/td>\r\n<td style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 99.2083px;height: 73px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt;margin-right: 5.5pt\">26.2742%<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 225.542px;height: 73px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt;margin-right: 5.5pt\">Finds the population coefficient of variation<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr class=\"TableNormal-R\" style=\"height: 46.8pt\">\r\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0.5pt 0.5pt 0.5pt 0pt;border-style: solid solid solid none;border-color: #a5a5a5 #a5a5a5 #a5a5a5 windowtext;padding: 0px 0pt;width: 33.0694px;height: 61px\">\r\n<p class=\"import-TableParagraph\" style=\"text-align: right;margin-right: 5.6pt\">8<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 80.1667px;height: 61px\">\r\n<p class=\"import-TableParagraph\">\u00a0 $50,000<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 139.292px;height: 61px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.15pt\">Coefficient of Variation (Sample)<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 235.5px;height: 61px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">=VAR.S(A2:A8) \/AVERAGE(A2:A8)<\/p>\r\n<\/td>\r\n<td style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 99.2083px;height: 61px\">\r\n<p class=\"import-TableParagraph\" style=\"text-align: justify;margin-left: 6.2pt;margin-right: 5.5pt\">28.7820%<\/p>\r\n<\/td>\r\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 225.542px;height: 61px\">\r\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt;margin-right: 5.5pt;text-align: left\">Finds the sample coefficient of variation<\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/04\/Measures-of-Variation_Formulae.xlsx\">Click here to download the Excel spreadsheet shown in the above table<\/a>\r\n\r\n<\/div>\r\n<h2 class=\"formulas\"><strong style=\"font-size: 20.5333px;text-align: initial\">Computing<\/strong>\u00a0<span style=\"font-size: 20.5333px\">Coefficient of Variation<\/span><\/h2>\r\n<ul>\r\n \t<li class=\"formulas\"><span style=\"font-size: 20.5333px;text-align: initial\">Usually, we find the average and standard deviation separately<\/span><\/li>\r\n \t<li class=\"formulas\"><span style=\"font-size: 20.5333px;text-align: initial\">We then divide the standard deviation by the mean (average) to calculate the coefficient of variation<\/span><\/li>\r\n \t<li class=\"formulas\"><span style=\"font-size: 20.5333px;text-align: initial\">Example: if we have the mean calculated in cell D9 and the sample standard deviation calculated in D4<\/span><\/li>\r\n \t<li class=\"formulas\"><span style=\"font-size: 20.5333px;text-align: initial\">Sample Coefficient of Variation <\/span><em style=\"font-size: 20.5333px;text-align: initial\">\u2192<\/em><span style=\"font-size: 20.5333px;text-align: initial\"> D4\/D9<\/span><\/li>\r\n \t<li>Note: It is recommended that you format the cell as a percentage and display 2 decimals<\/li>\r\n<\/ul>","rendered":"<div class=\"formulas\">\n<p class=\"import-Normal\"><strong><code><\/code><\/strong><\/p>\n<h2 class=\"import-Normal\"><strong>Excel<\/strong> <strong>Commands<\/strong><\/h2>\n<table style=\"width: 819px;height: 398px\">\n<tbody>\n<tr class=\"TableNormal-R\" style=\"height: 18pt\">\n<td class=\"TableNormal-C\" style=\"border-width: 0pt 0.5pt 0.5pt 0pt;border-style: none solid solid none;border-color: windowtext #a5a5a5 #a5a5a5 windowtext;padding: 0px 0pt;width: 33.0694px;height: 36px\">\n<p class=\"import-TableParagraph\">\n<\/td>\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0pt 0.5pt 0.5pt;border-style: none solid solid;border-color: windowtext #a5a5a5 #a5a5a5;padding: 0px 0pt;width: 80.1667px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.1pt\">A<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0pt 0.5pt 0.5pt;border-style: none solid solid;border-color: windowtext #a5a5a5 #a5a5a5;padding: 0px 0pt;width: 139.292px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.15pt\">B<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0pt 0.5pt 0.5pt;border-style: none solid solid;border-color: windowtext #a5a5a5 #a5a5a5;padding: 0px 0pt;width: 235.5px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">C<\/p>\n<\/td>\n<td style=\"background-color: #bfbfbf;border-width: 0pt 0.5pt 0.5pt;border-style: none solid solid;border-color: windowtext #a5a5a5 #a5a5a5;padding: 0px 0pt;width: 99.2083px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">D<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0pt 0.5pt 0.5pt;border-style: none solid solid;border-color: windowtext #a5a5a5 #a5a5a5;padding: 0px 0pt;width: 225.542px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">E<\/p>\n<\/td>\n<\/tr>\n<tr class=\"TableNormal-R\" style=\"height: 17.95pt\">\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0.5pt 0.5pt 0.5pt 0pt;border-style: solid solid solid none;border-color: #a5a5a5 #a5a5a5 #a5a5a5 windowtext;padding: 0px 0pt;width: 33.0694px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"text-align: right;margin-right: 5.6pt\">1<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"background-color: #fffbcc;padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 80.1667px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.1pt\"><strong>X<\/strong><\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"background-color: #fffbcc;padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 139.292px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.15pt\"><strong>Name<\/strong><\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"background-color: #fffbcc;padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 235.5px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\"><strong>Command<\/strong><\/p>\n<\/td>\n<td style=\"background-color: #fffbcc;padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 99.2083px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\"><strong>Answer<\/strong><\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"background-color: #fffbcc;padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 225.542px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\"><strong>Answer (with Notes)<\/strong><\/p>\n<\/td>\n<\/tr>\n<tr class=\"TableNormal-R\" style=\"height: 17.95pt\">\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0.5pt 0.5pt 0.5pt 0pt;border-style: solid solid solid none;border-color: #a5a5a5 #a5a5a5 #a5a5a5 windowtext;padding: 0px 0pt;width: 33.0694px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"text-align: right;margin-right: 5.6pt\">2<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 80.1667px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.1pt\">$20,000<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 139.292px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.15pt\">Range<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 235.5px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">=MAX(A2:A8)-MIN(A2:A8)<\/p>\n<\/td>\n<td style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 99.2083px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">$25,000<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 225.542px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">Finds the range<\/p>\n<\/td>\n<\/tr>\n<tr class=\"TableNormal-R\" style=\"height: 17.95pt\">\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0.5pt 0.5pt 0.5pt 0pt;border-style: solid solid solid none;border-color: #a5a5a5 #a5a5a5 #a5a5a5 windowtext;padding: 0px 0pt;width: 33.0694px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"text-align: right;margin-right: 5.6pt\">3<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 80.1667px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.1pt\">$25,000<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 139.292px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.15pt\">Population Standard Deviation<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 235.5px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">=STDEV.P(A2:A8)<\/p>\n<\/td>\n<td style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 99.2083px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">$8,539.13<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 225.542px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">Finds the population standard deviation<\/p>\n<\/td>\n<\/tr>\n<tr class=\"TableNormal-R\" style=\"height: 32.4pt\">\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0.5pt 0.5pt 0.5pt 0pt;border-style: solid solid solid none;border-color: #a5a5a5 #a5a5a5 #a5a5a5 windowtext;padding: 0px 0pt;width: 33.0694px;height: 42px\">\n<p class=\"import-TableParagraph\" style=\"text-align: right;margin-right: 5.6pt\">4<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 80.1667px;height: 42px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.1pt\">$30,000<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 139.292px;height: 42px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.15pt\">Sample Standard Deviation<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 235.5px;height: 42px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">=STDEV.S(A2:A8)<\/p>\n<\/td>\n<td style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 99.2083px;height: 42px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt;margin-right: 5.55pt\">$9,354.14<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 225.542px;height: 42px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt;margin-right: 5.55pt\">Finds the sample standard deviation<\/p>\n<\/td>\n<\/tr>\n<tr class=\"TableNormal-R\" style=\"height: 32.4pt\">\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0.5pt 0.5pt 0.5pt 0pt;border-style: solid solid solid none;border-color: #a5a5a5 #a5a5a5 #a5a5a5 windowtext;padding: 0px 0pt;width: 33.0694px;height: 42px\">\n<p class=\"import-TableParagraph\" style=\"text-align: right;margin-right: 5.6pt\">5<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 80.1667px;height: 42px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.1pt\">$35,000<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 139.292px;height: 42px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.15pt\">Population Variance<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 235.5px;height: 42px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">=VAR.P(A2:A8)<\/p>\n<\/td>\n<td style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 99.2083px;height: 42px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt;margin-right: 5.55pt\">72,916,667<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 225.542px;height: 42px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt;margin-right: 5.55pt\">Finds the population variance<\/p>\n<\/td>\n<\/tr>\n<tr class=\"TableNormal-R\" style=\"height: 17.95pt\">\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0.5pt 0.5pt 0.5pt 0pt;border-style: solid solid solid none;border-color: #a5a5a5 #a5a5a5 #a5a5a5 windowtext;padding: 0px 0pt;width: 33.0694px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"text-align: right;margin-right: 5.6pt\">6<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 80.1667px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.1pt\">$40,000<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 139.292px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.15pt\">Sample Variance<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 235.5px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">=VAR.S(A2:A8)<\/p>\n<\/td>\n<td style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 99.2083px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">87,500,000<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 225.542px;height: 36px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">Finds the sample variance<\/p>\n<\/td>\n<\/tr>\n<tr class=\"TableNormal-R\" style=\"height: 46.8pt\">\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0.5pt 0.5pt 0.5pt 0pt;border-style: solid solid solid none;border-color: #a5a5a5 #a5a5a5 #a5a5a5 windowtext;padding: 0px 0pt;width: 33.0694px;height: 73px\">\n<p class=\"import-TableParagraph\" style=\"text-align: right;margin-right: 5.6pt\">7<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 80.1667px;height: 73px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.1pt\">$45,000<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 139.292px;height: 73px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.15pt;margin-right: 6.25pt\">Coefficient of Variation (Population)<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 235.5px;height: 73px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">=VAR.P(A2:A8) \/AVERAGE(A2:A8)<\/p>\n<\/td>\n<td style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 99.2083px;height: 73px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt;margin-right: 5.5pt\">26.2742%<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 225.542px;height: 73px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt;margin-right: 5.5pt\">Finds the population coefficient of variation<\/p>\n<\/td>\n<\/tr>\n<tr class=\"TableNormal-R\" style=\"height: 46.8pt\">\n<td class=\"TableNormal-C\" style=\"background-color: #bfbfbf;border-width: 0.5pt 0.5pt 0.5pt 0pt;border-style: solid solid solid none;border-color: #a5a5a5 #a5a5a5 #a5a5a5 windowtext;padding: 0px 0pt;width: 33.0694px;height: 61px\">\n<p class=\"import-TableParagraph\" style=\"text-align: right;margin-right: 5.6pt\">8<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 80.1667px;height: 61px\">\n<p class=\"import-TableParagraph\">\u00a0 $50,000<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 139.292px;height: 61px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.15pt\">Coefficient of Variation (Sample)<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 235.5px;height: 61px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt\">=VAR.S(A2:A8) \/AVERAGE(A2:A8)<\/p>\n<\/td>\n<td style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 99.2083px;height: 61px\">\n<p class=\"import-TableParagraph\" style=\"text-align: justify;margin-left: 6.2pt;margin-right: 5.5pt\">28.7820%<\/p>\n<\/td>\n<td class=\"TableNormal-C\" style=\"padding: 0px 0pt;border: 0.5pt solid #a5a5a5;width: 225.542px;height: 61px\">\n<p class=\"import-TableParagraph\" style=\"margin-left: 6.2pt;margin-right: 5.5pt;text-align: left\">Finds the sample coefficient of variation<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/04\/Measures-of-Variation_Formulae.xlsx\">Click here to download the Excel spreadsheet shown in the above table<\/a><\/p>\n<\/div>\n<h2 class=\"formulas\"><strong style=\"font-size: 20.5333px;text-align: initial\">Computing<\/strong>\u00a0<span style=\"font-size: 20.5333px\">Coefficient of Variation<\/span><\/h2>\n<ul>\n<li class=\"formulas\"><span style=\"font-size: 20.5333px;text-align: initial\">Usually, we find the average and standard deviation separately<\/span><\/li>\n<li class=\"formulas\"><span style=\"font-size: 20.5333px;text-align: initial\">We then divide the standard deviation by the mean (average) to calculate the coefficient of variation<\/span><\/li>\n<li class=\"formulas\"><span style=\"font-size: 20.5333px;text-align: initial\">Example: if we have the mean calculated in cell D9 and the sample standard deviation calculated in D4<\/span><\/li>\n<li class=\"formulas\"><span style=\"font-size: 20.5333px;text-align: initial\">Sample Coefficient of Variation <\/span><em style=\"font-size: 20.5333px;text-align: initial\">\u2192<\/em><span style=\"font-size: 20.5333px;text-align: initial\"> D4\/D9<\/span><\/li>\n<li>Note: It is recommended that you format the cell as a percentage and display 2 decimals<\/li>\n<\/ul>\n","protected":false},"author":865,"menu_order":5,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-517","chapter","type-chapter","status-publish","hentry"],"part":22,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/517","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/users\/865"}],"version-history":[{"count":6,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/517\/revisions"}],"predecessor-version":[{"id":524,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/517\/revisions\/524"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/parts\/22"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/517\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/media?parent=517"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapter-type?post=517"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/contributor?post=517"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/license?post=517"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}