In my class 10 book I got to know a formula of finding mode in grouped frequency distribution table. That formula is
L+ (f1-f0)\ (2f1-f0-f2)× H
Where,
L is the lower limit of modal class
f1 is the frequency of modal class
f2 is frequency of exceeding class of modal class
f0 is frequency of preeceding class of modal class
H is the width of each class.
But my doubt is if we calculate according to above equation then answer that is the mode will alwats lie in modal class. But I think it shouldn't be true all the time.
Example
Some information here on occurence of number 1,1,2,3,3,3,3,3,3,5,5,5,6,6,6,6,7,7,7,7,8,8,8,8
Here 1×2times
2×1time
3×6times
5×3times
6×4times
7×4times
8×4times
A table of data here
Class frequency 0-3 3 3-6 9 6-9 12
Now if we calculate through formulae we got something 6.6 (which you can notice is again from modal class) But can you notice that 6.6 isn't even the number in originol data. And also 3 is the actual mode. But just because overall frequency is more in 6-9 class we consider mode to exist in this class.
So this formulae show wrong result sonetime and can't be practical all time.
So are there only conditions and assumptions in which case this formulae applied??
Derivation of Mode of grouped data (look at its 1st answer's comment No. 4 by @DARK)
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