How to Calculate Standard Deviation

&NewLine;<&excl;-- WP QUADS Content Ad Plugin v&period; 2&period;0&period;95 -->&NewLine;<div class&equals;"quads-location quads-ad1" id&equals;"quads-ad1" style&equals;"float&colon;left&semi;margin&colon;0px 0px 0px 0&semi;">&NewLine;&NewLine;<&sol;div>&NewLine;<p align&equals;"justify">Standard deviation is the most widely used measure of dispersion&period; It is defined as the positive square root of sum of the square deviation of the variable from its mean divided by total number of observations&period; In other words it is the positive square root of a quantity called variance&period; Standard deviation is a very useful measure of dispersion&period; The importance of standard deviation can be highlighted with help of simple example&period; For example company A has average annual profit of &dollar;10000 with a standard deviation of &dollar;3000 and company B has average annual profit of &dollar;10000 with standard deviation of &dollar;6000&period; Now because the standard deviation of company A is only 3000 which indicates that the annual returns of company A fluctuate from &dollar;7000 to &dollar;13000 &lpar;10000-3000&equals;7000&comma; 10000&plus;3000&equals;13000&rpar;&&num;160&semi; whereas annual returns of company B fluctuate from &dollar;4000 to &dollar;16000&period; Therefore company A is more stable and less risky than company B&period;<&sol;p>&NewLine;<p align&equals;"justify">&NewLine;The calculation of standard deviation for ungrouped data is different from the grouped data&period; Similarly there is also difference in the formulas for sample data and population data&period; These formulas are given below&period;<&sol;p>&NewLine;<p align&equals;"justify">&&num;160&semi;<&sol;p>&NewLine;<p> <strong>Formulas for Ungrouped Data<&sol;strong><&sol;p>&NewLine;<p> <strong><&sol;strong><&sol;p>&NewLine;<p> <strong><&sol;strong><&sol;p>&NewLine;<&excl;-- WP QUADS Content Ad Plugin v&period; 2&period;0&period;95 -->&NewLine;<div class&equals;"quads-location quads-ad2" id&equals;"quads-ad2" style&equals;"float&colon;none&semi;margin&colon;0px 0 0px 0&semi;text-align&colon;center&semi;">&NewLine;&NewLine;<&sol;div>&NewLine;&NewLine;<p> <strong><&sol;strong><&sol;p>&NewLine;<p> <strong><&sol;strong><&sol;p>&NewLine;<p> <a href&equals;"http&colon;&sol;&sol;mba-lectures&period;com&sol;wp-content&sol;uploads&sol;2010&sol;06&sol;image82&period;png"><img title&equals;"image" style&equals;"border-top-width&colon; 0px&semi; display&colon; inline&semi; border-left-width&colon; 0px&semi; border-bottom-width&colon; 0px&semi; border-right-width&colon; 0px" height&equals;"274" alt&equals;"image" src&equals;"http&colon;&sol;&sol;mba-lectures&period;com&sol;wp-content&sol;uploads&sol;2010&sol;06&sol;image&lowbar;thumb82&period;png" width&equals;"350" border&equals;"0" &sol;><&sol;a> <&sol;p>&NewLine;<p> &&num;160&semi;<&sol;p>&NewLine;<p> <strong>Formulas for Grouped Data<&sol;strong><&sol;p>&NewLine;<p> &&num;160&semi;<&sol;p>&NewLine;<p> <strong><&sol;strong><&sol;p>&NewLine;<p> <a href&equals;"http&colon;&sol;&sol;mba-lectures&period;com&sol;wp-content&sol;uploads&sol;2010&sol;06&sol;image83&period;png"><img title&equals;"image" style&equals;"border-top-width&colon; 0px&semi; display&colon; inline&semi; border-left-width&colon; 0px&semi; border-bottom-width&colon; 0px&semi; border-right-width&colon; 0px" height&equals;"267" alt&equals;"image" src&equals;"http&colon;&sol;&sol;mba-lectures&period;com&sol;wp-content&sol;uploads&sol;2010&sol;06&sol;image&lowbar;thumb83&period;png" width&equals;"350" border&equals;"0" &sol;><&sol;a> <&sol;p>&NewLine;<p> &&num;160&semi;<&sol;p>&NewLine;<p> <strong>Calculation of Standard Deviation for Ungrouped Data<&sol;strong><&sol;p>&NewLine;<p> &&num;160&semi;<&sol;p>&NewLine;<p> <strong><&sol;strong>&NewLine;<&excl;-- WP QUADS Content Ad Plugin v&period; 2&period;0&period;95 -->&NewLine;<div class&equals;"quads-location quads-ad3" id&equals;"quads-ad3" style&equals;"float&colon;none&semi;margin&colon;0px&semi;">&NewLine;&NewLine;<&sol;div>&NewLine;&NewLine;