Mode: Derivation

[rktpro]

The mode for grouped data

You can calculate the mode for a grouped frequency table by using the following formula:

 

 

 

 

 

Where:

• L is the lower class boundary of the modal class.
• f_m is the frequency associated with the modal class.
• f₁ is the frequency of the class before to the modal class.
• f2 is the frequency of the class after the modal class.
• h is the difference between the upper and lower bounds of the modal class.

I want to know how this has been derived? If I know it I can be able to say why class preceding a class and following a class have an effect on the mode. Thanks.

[rktpro]

Anyone, please? Any idea about approaching the question?

[khaled]

Anyone, please? Any idea about approaching the question?

 

[math]Mode \; = \; L + ( \frac{ (f_m - f_1) }{ (f_m - f_1) + (f_m - f_2) } \times h )[/math]

 

See: Wikipedia: Derivative

[rktpro]

Khaled: That Wikipedia article is too complex for my level. Could you conclude from that, please?

[imatfaal]

rktpro

 

This really isn't my scene - but to get the ball rolling and discussion going. The mode is the most common observation - but when grouped frequencies are used it is the most commonly observed category. To get a single figure - rather than a group - you can use the above calculation, but it is an approximation.

 

in very simplistic terms you are judging how far though the modal category your single figure mode lies - you do this by taking the beginning of the category (L) and adding on a proportion of the width of the category (h). this proportion that you add on (fm-f1)/[(fm-f1)+(fm-f2)] is very basically how much bigger the mode cat is than the previous category, compared to the sum of the differences to the previous and next category.

 

examples - if the category 9 is the modal category, and cat8 frequency is just a bit smaller and cat 10 is tiny; then the mode will be at the lower end of cat 9. if cat 8 and cat 10 are equal then the mode will be in the middle of cat9 etc.

 

Sorry above a bit rambling - hope it gets things started.

 

and Khaled - a link to a page on calculus purely because the OP included the word derived??

[rktpro]

rktpro

 

This really isn't my scene - but to get the ball rolling and discussion going. The mode is the most common observation - but when grouped frequencies are used it is the most commonly observed category. To get a single figure - rather than a group - you can use the above calculation, but it is an approximation.

 

in very simplistic terms you are judging how far though the modal category your single figure mode lies - you do this by taking the beginning of the category (L) and adding on a proportion of the width of the category (h). this proportion that you add on (fm-f1)/[(fm-f1)+(fm-f2)] is very basically how much bigger the mode cat is than the previous category, compared to the sum of the differences to the previous and next category.

 

examples - if the category 9 is the modal category, and cat8 frequency is just a bit smaller and cat 10 is tiny; then the mode will be at the lower end of cat 9. if cat 8 and cat 10 are equal then the mode will be in the middle of cat9 etc.

 

Sorry above a bit rambling - hope it gets things started.

 

and Khaled - a link to a page on calculus purely because the OP included the word derived??

 

That was really helpful. Thanks!

[rktpro]

rktpro

 

This really isn't my scene - but to get the ball rolling and discussion going. The mode is the most common observation - but when grouped frequencies are used it is the most commonly observed category. To get a single figure - rather than a group - you can use the above calculation, but it is an approximation.

 

in very simplistic terms you are judging how far though the modal category your single figure mode lies - you do this by taking the beginning of the category (L) and adding on a proportion of the width of the category (h). this proportion that you add on (fm-f1)/[(fm-f1)+(fm-f2)] is very basically how much bigger the mode cat is than the previous category, compared to the sum of the differences to the previous and next category.

 

examples - if the category 9 is the modal category, and cat8 frequency is just a bit smaller and cat 10 is tiny; then the mode will be at the lower end of cat 9. if cat 8 and cat 10 are equal then the mode will be in the middle of cat9 etc.

 

Sorry above a bit rambling - hope it gets things started.

 

and Khaled - a link to a page on calculus purely because the OP included the word derived??

 

Do you know who gave this formula?

[imatfaal]

No sorry - as I said I am no expert, in truth I looked at it and ran a few examples to work out what it meant - whether I have ever seen it before is doubtful