How to Calculate Harmonic Mean

&NewLine;<&excl;-- WP QUADS Content Ad Plugin v&period; 2&period;0&period;92 -->&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>The harmonic mean of a set of observations is the reciprocal of the arithmetic mean of the reciprocal of the observations&period; Harmonic mean is defined only for non-zero positive values and is used for averaging while keeping one variable constant&period; For example in first test a typist types 400 words in 50 minutes&comma; in second test he types the same words &lpar;400&rpar; in 40 minutes and in third test he takes 30 minutes to type the 400 words&period; Determine his average speed for the three tests&period;  &lpar;Note here constant variable is 400 words&rpar;&period;<&sol;p>&NewLine;<p>Therefore&comma;<&sol;p>&NewLine;<p><a href&equals;"http&colon;&sol;&sol;mba-lectures&period;com&sol;wp-content&sol;uploads&sol;2010&sol;05&sol;image29&period;png"><img style&equals;"display&colon; inline&semi; border-width&colon; 0px&semi;" title&equals;"image" src&equals;"http&colon;&sol;&sol;mba-lectures&period;com&sol;wp-content&sol;uploads&sol;2010&sol;05&sol;image&lowbar;thumb29&period;png" border&equals;"0" alt&equals;"image" width&equals;"350" height&equals;"46" &sol;><&sol;a><&sol;p>&NewLine;<p>The calculation of H&period;M for the ungrouped data is slightly different from that of grouped data&period; Calculations for both types of data are given below&period;<&sol;p>&NewLine;<h3>Harmonic Mean of Ungrouped Data<&sol;h3>&NewLine;<p>In order to calculate the harmonic mean of ungrouped data the formula will be&colon;<&sol;p>&NewLine;<p><a href&equals;"http&colon;&sol;&sol;mba-lectures&period;com&sol;wp-content&sol;uploads&sol;2010&sol;05&sol;image30&period;png"><img style&equals;"display&colon; inline&semi; border-width&colon; 0px&semi;" title&equals;"image" src&equals;"http&colon;&sol;&sol;mba-lectures&period;com&sol;wp-content&sol;uploads&sol;2010&sol;05&sol;image&lowbar;thumb30&period;png" border&equals;"0" alt&equals;"image" width&equals;"92" height&equals;"38" &sol;><&sol;a><&sol;p>&NewLine;<&excl;-- WP QUADS Content Ad Plugin v&period; 2&period;0&period;92 -->&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>Here&comma;<&sol;p>&NewLine;<p>N is the total number of observations<br &sol;>&NewLine;And x represents the values of observations while &quest;1&sol;x shows the sum of reciprocal of observations&period;<br &sol;>&NewLine;<strong>Problem&colon;<&sol;strong> During one month the total number of kilometers driven by each truck is given below&period; Find the geometric mean&period;<&sol;p>&NewLine;<p><a href&equals;"http&colon;&sol;&sol;mba-lectures&period;com&sol;wp-content&sol;uploads&sol;2010&sol;05&sol;image31&period;png"><img style&equals;"display&colon; inline&semi; border-width&colon; 0px&semi;" title&equals;"image" src&equals;"http&colon;&sol;&sol;mba-lectures&period;com&sol;wp-content&sol;uploads&sol;2010&sol;05&sol;image&lowbar;thumb31&period;png" border&equals;"0" alt&equals;"image" width&equals;"350" height&equals;"241" &sol;><&sol;a><&sol;p>&NewLine;<h3>Harmonic Mean of grouped Data<&sol;h3>&NewLine;<p>Harmonic mean of grouped data can be calculated with the help of following formula&colon;<&sol;p>&NewLine;<p><a href&equals;"http&colon;&sol;&sol;mba-lectures&period;com&sol;wp-content&sol;uploads&sol;2010&sol;05&sol;image32&period;png"><img style&equals;"display&colon; inline&semi; border-width&colon; 0px&semi;" title&equals;"image" src&equals;"http&colon;&sol;&sol;mba-lectures&period;com&sol;wp-content&sol;uploads&sol;2010&sol;05&sol;image&lowbar;thumb32&period;png" border&equals;"0" alt&equals;"image" width&equals;"106" height&equals;"48" &sol;><&sol;a><&sol;p>&NewLine;<p>Here&comma;<&sol;p>&NewLine;<p>N is the sum of all frequencies<br &sol;>&NewLine;f is the frequency corresponding to each observation x while &quest;f&sol;x represents the sum of reciprocal of grouped observations&period;<&sol;p>&NewLine;<p><strong>Problem&colon;<&sol;strong> Following is the frequency distribution of the marks &lpar;out of 40&rpar; obtained by the students of a certain college in statistics&period; Calculate harmonic mean&period;<&sol;p>&NewLine;<p><a href&equals;"http&colon;&sol;&sol;mba-lectures&period;com&sol;wp-content&sol;uploads&sol;2010&sol;05&sol;image33&period;png"><img style&equals;"display&colon; inline&semi; border-width&colon; 0px&semi;" title&equals;"image" src&equals;"http&colon;&sol;&sol;mba-lectures&period;com&sol;wp-content&sol;uploads&sol;2010&sol;05&sol;image&lowbar;thumb33&period;png" border&equals;"0" alt&equals;"image" width&equals;"500" height&equals;"278" &sol;><&sol;a>&NewLine;<&excl;-- WP QUADS Content Ad Plugin v&period; 2&period;0&period;92 -->&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;